An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of (...) the issue under study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

In this study, two modified gradient descent algorithms are proposed for time-delayed models. To estimate the parameters and time-delay simultaneously, a redundant rule method is introduced, which turns the time-delayed model into an augmented model. Then, two GD algorithms can be used to identify the time-delayed model. Compared with the traditional GD algorithms, these two modified GD algorithms have the following advantages: avoid a high-order matrix eigenvalue calculation, thus, are more efficient for large-scale systems; have faster convergence (...) rates, therefore, are more practical in engineering practices. The convergence properties and simulation examples are presented to illustrate the efficiency of the two algorithms. (shrink)

Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions [Shimizu et al. 2006; Hoyer et al. 2009; Zhang and Hyvärinen 2009b]. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian acyclic model, nonlinear additive noise model, and post-nonlinear model. Currently, there are two ways to estimate (...) the parameters in the models: dependence minimization and maximum likelihood. In this article, we show that for any acyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons; we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims. (shrink)

Tim van Gelder, following Brandom, Collins and others, uses the so‐called wide content of capacities which support social, norm governed activities, such as language, to argue for their anti‐natural, abstract, but socially instituted nature and thence for the failure of the entire traditional mind‐body discussion as ill‐posed. We argue that his former conclusion is wrong, that such properties are naturalisable, complicated organisational properties of the complexly organised, non‐linearly interactive systems that human beings are. This analysis also provides principled support, but (...) on other grounds, for van Gelder’s latter conclusion. We outline a new naturalist approach to the organisational capacities of such systems that is intended to ground their biological, cognitive and social characters. (shrink)

The models of the electric charge and magnetic moment are presented based on the nonlinear response of a vacuum on the applied electric and magnetic fields. The model of the electric charge contains one parameter—the radius of charge—and predicts one value of the electric charge for all elementary particles independently on the value of this radius. Different values of this parameter for the electron are discussed.

A theoretical model is presented for pattern formation in an epithelium. The epithelial model consists of a thin, incompressible, viscoelastic membrane on an elastic foundation (substrate), with the component cells assumed to have active contractile properties similar to those of smooth muscle. The analysis includes the effects of large strains and material nonlinearity, and the governing equations were solved using finite differences. Deformation patterns form when the cells activate while lying on the descending limb of their total (active (...) + passive) stress-stretch curve. Various one-dimensional and two-dimensional simulations illustrate the effects of spatial and temporal variations in passive stiffness, as well as the effects of foundation stiffness and stretch activation. The model can be used to examine the mechanical aspects of pattern formation in morphogenetic processes such as angiogenesis and myocardial trabeculation. (shrink)

A model predictive control method based on recursive backpropagation neural network and genetic algorithm is proposed for a class of nonlinear systems with time delays and uncertainties. In the offline modeling stage, a multistep-ahead predictor with GA-RBP neural network is designed, where GA-BP neural network is used as a one-step prediction model and GA is employed to train the initial weights and bias of the BP neural network. The incorporation of GA into RBP can reduce the possibility (...) of the BP neural network falling into a local optimum instead of reaching global optimization. In the online optimizing stage, a multistep-ahead GA-RBP neural network predictor and an improved gradient descent method are proposed to efficiently solve the online optimization problem of nonlinear MPC by minimizing a modified quadratic criterion. The designed MPC strategy can avoid information loss while linearizing the controlled system and computing the Hessian matrix and its inverse matrix. Experimental results show that the proposed approach can reduce the computational burden and improve the performance of MPC for the solution of nonlinear controlled systems. (shrink)

The present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno model via the sector nonlinearity transformation. A proportional multiple integral observer based on the TS model is designed to estimate (...) simultaneously the state vector and the unknown input. The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer. (shrink)

The comparison between two nonlinear duopoly models constructed based on symmetric utility function that is derived from Cobb–Douglas is investigated in this paper. The first model consists of two firms which update their outputs using gradient-based mechanism called bounded rationality. The second model contains a bounded rational firm that is competing with a firm whose outputs depend on a trade-off between market share maximization and profit maximization. For the two models, the fixed points are calculated and their (...) conditions of stability are analyzed. The obtained results show that the second model is more stabilizing provided that the second firm adopts low weights of trade-offs. We show that the two models can be destabilized via flip bifurcation only. Furthermore, the noninvertibility of the two models that can give rise to several stable attractors is discussed. (shrink)

With renewable energy being increasingly connected to power grids, pumped storage plants play a very important role in restraining the fluctuation of power grids. However, conventional control strategy could not adapt well to the different control tasks. This paper proposes an intelligent nonlinear model predictive control strategy, in which hydraulic-mechanical and electrical subsystems are combined in a synchronous control framework. A newly proposed online sequential extreme learning machine algorithm with forgetting factor is introduced to learn the dynamic behaviors (...) of the coupling system. Specifically, the initial learning parameters are optimized by prior-knowledge learning and a new self-adaptive adjustment strategy is also put forward. Subsequently, the stair-like control strategy and artificial sheep algorithm are used in rolling the optimization mechanism to replace the existing complex differential geometric solutions. Comparative experiments are carried out under different working conditions based on a PSP in China. The results show that the influence from coupling factors can be considerable and the proposed MPC strategy indicates superiority in voltage and load adjustment as well as the frequency oscillation suppression. (shrink)

After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in futility. The complex-systems (...) approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches. (shrink)

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse (...) nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness. (shrink)

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

Ever wonder if it is possible to construct a numeric scale for environmental variables, like one does for the temperature? This paper is an attempt to construct one. There are two main parts: section “Statistical Analysis of Variations” presents a general statistical strategy for environmental factor selection. Section “Nonlinear Analytical Geometric Model of Variations” develops an analytical geometric representation of system variations in response to environmental changes. The model is used to quantify the effects of environmental interactions. (...) The paper treats only one-dimensional case, however, the derivation of the case of multiple independent factors follows immediately. The general method developed in this paper may prove applicable to many different fields, such as extensions beyond classical physics, economics, and other sciences. Section “Conclusion” provides an illustration of applications, examples and implications of the results. (shrink)

Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a (...) nonlinear pulse term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models. (shrink)

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of (...) variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery. (shrink)

We consider an integrable, nonlocal and nonlinear, Schrödinger equation as a model for building space–time patchings in inhomogeneous loop quantum cosmology. We briefly review exact solutions of the NNSE, specially those obtained through “geometric equivalence” methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of (...) all phase portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue-type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue-type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be (...) the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

Whether financial inclusion and economic growth can sustainably release poverty alleviation effects in long term has been the focus of academia and government sector. This article uses provincial panel data from 2004 to 2019 to examine the dynamic nonlinear connectedness between the financial inclusion, economic growth, income inequality, and poverty alleviation; the main objective is to reveal the direction and intensity of the long-term and short-term impact of each factor on poverty alleviation. By building a panel vector autoregression (...) class='Hi'>model, the comparison analyses of national, eastern, central, and western sample groups verify the existence of dynamic nonlinear connectedness among the four variables. The study found that there is complex bidirectional causality between these variables, financial inclusion has the long-term impact on promoting poverty alleviation in China, the impact of economic growth is relatively weak, and income inequality has weakened the positive impact of financial inclusion on poverty alleviation. Through the analysis of impulse response function, variance decomposition, and time-varying nonparametric estimates in different economic regions, we find that the impact of financial inclusion on poverty alleviation presents a U-shaped characteristic, and the contribution of financial inclusion to poverty alleviation in western regions is significant, but poverty reduction in eastern and central region mainly depends on economic growth. For policymakers, financial inclusion can be an effective way to alleviate relative poverty, but the poverty governance should focus more on reducing income inequality in China. (shrink)

According to resource limitation, a more realistic pest management is that the impulsive control actions should be adjusted according to the densities of both pest and natural enemy in the field, which result in nonlinear impulsive control. Therefore, we have proposed a Beddington–DeAngelis interference predator-prey model concerning integrated pest management with both density-dependent pest and natural enemy population. We find that the pest-eradication periodic solution is globally stable if the impulsive period is less than the critical value by (...) Floquet theorem. The condition of permanent is established, and a stable positive periodic solution appears via a supercritical bifurcation by bifurcation theorem. Finally, in order to investigate the effects of those nonlinear control strategies on the successful pest control, the bifurcation diagrams showed that the model exists with very complex dynamics. Consequently, the resource limitation may result in pest outbreak in complex ways, which means that the pest control strategies should be carefully designed. (shrink)

Three principles of dialectical analysis are examined in terms of nonlinear dynamics models. The three principles are the transformation of quantity into quality, the interpenetration of opposites, and the negation of the negation. The first two of these especially are interpreted within the frameworks of catastrophe, chaos, and emergent dynamics complexity theoretic models, with the concept of bifurcation playing a central role. Problems with this viewpoint are also discussed.

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. 11 (...) EUCh. These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship (...) connecting coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called “effective” and “tired” photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest. (shrink)

The challenges posed by chronic illness have pointed out to epidemiologists the multifactorial complex nature of disease causality. This notion has been referred to as a web of causality. This web extends theoretically beyond risk markers. It includes determinants of emergence/non-emergence of disease. This web of determinants is a form of complex system. Due to its complexity, the determinants within such system are not linked to each others in a linear, predictable manner only. Predictability is possible only on a short-term (...) basis, and unpredictability sets in over the long run. Understanding such a system of determinants calls for articulation and testing of complex models which synthesize our knowledge of multiple determinants at many scales, both biological and otherwise. Given the complexity of this web and existing knowledge about the nonlinearity of such systems, the following question is posed: Can the challenge of studying causality be adequately addressed if emphasis continues to be placed on using tools and methods that are geared towards looking at such system from a linear paradigm? Or is it time to add to the epidemiologic research agenda the notion of nonlinearity and its relevant form of analytical approaches that are being tested in other disciplines? Furthermore, the question posed here applies as well to the study of determinants of health. Addressing determinants of heath adds further complexity to our task. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution to the (...) discussion is unlikely to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

This paper presents a nonlinear trajectory controller with improved performances for a general model of the waverider based on feedback linearization theory and composite nonlinear feedback technique. First, a nonlinear controller is presented using the dynamic inversion and CNF technique for the MIMO Model, and the robust stability of the proposed controller is proved. Then, the nonlinear model is established on the basis of hypersonic aerodynamic principle, and the dynamic characteristics are analyzed accordingly, (...) and the periodic trajectory is designed and optimized in combination with a fuel optimization problem. Furthermore, the nonlinear controller is applied to the trajectory tracking of the waverider model, and the general design steps are provided the flight controller using this nonlinear control method. Finally, an illustrative example is given to verify the effectiveness of the nonlinear controller of the waverider, and the flight performances are improved accordingly, including system stability, robustness, and tracking ability. (shrink)

Using the genetic algorithm and fuzzy logic, this study presents a nonlinear approach to the evaluation of biofunctional intelligence. According to the biofunctional model, intelligence may be viewed as a multisource phenomenon resulting in part from the interaction of learning processes and sources of self-regulation. Learning processes are regulated by three sources of control , producing three subprocesses for each learning process. This paper examines the role of five such subprocesses as contributors to intelligence. Fuzzy logic captures the (...) fuzzy nature of human intelligence with GA providing a method for determining and optimizing the contribution of these learning subprocesses. (shrink)

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 1. Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

Study of electroencephalographic brain activity in behaving animals has guided development of a model for the self-organization of goal-directed behavior. Synthesis of a dynamical representation of brain function is based in the concept of intentionality as the organizing principle of animal and human behavior. The constructions of patterns of brain activity constitute meaning and not information or representations. The three accepted meanings of intention: "aboutness," goal-seeking, and wound healing, can be incorporated into the dynamics of meaningful behavior, centered in (...) the limbic system interacting with the sensory and motor systems. Evidence is noted for the maintenance in cortical neuropil of a felt work of synaptic connections, that have incorporated past experience by changes in learning, and that act as a unified whole in shaping each intentional action at each moment. This constitutes the intentional structure of the brain. Meaning is a focus having a place without edges in this structure. The focus continually moves through it along a chaotic trajectory; the meaning occupies the whole structure. In this view, consciousness is the active state of an intentional structure, and awareness is the subjective aspect of the shifting focus. (shrink)

In this paper, we propose a new predator-prey nonlinear dynamic evolutionary model of real estate enterprises considering the large, medium, and small real estate enterprises for three different prey teams. A 5D predator-prey nonlinear dynamic evolutionary system in the real estate market is established, where the large, medium, and small real estate enterprises correspond to three differential equations, provincial and local officials, and the central government correspond to the other two differential equations. Nonlinear dynamic analysis on (...) a 5D predator-prey evolutionary system in the real estate market, containing the analysis of equilibrium points and stabilities, is made. The corresponding discrete system is simulated, and the simulation results about Lyapunov spectrum, bifurcation diagram, sequence diagram, and phase diagram are given. Compared with the work of Yang et al. in which all real estate enterprises corresponded to one differential equation, in our proposed model, the large, medium, and small real estate enterprises correspond to three differential equations which is more accordant with the specific circumstance of real estate companies. (shrink)

We present the historical development of Nonlinear Dynamical Astronomy with emphasis on the “third integral” and its applications. The new era started with the use of computers, and of formal analytical developments in the spirit of Poincaré. Most dynamical systems were found to contain both ordered and chaotic orbits. The transition from order to chaos is discussed. Recent developments refer to the dynamical spectra, integrals of notion in self-consistent models, systems of 3 or more degrees of freedom, chaos in (...) relativity and cosmology, and chaos in quandum mechanics. (shrink)

Five experiments investigated the role of spatial connectedness between a pair of objects presented in the change detection task for the actual capacity of visual working memory (VWM) in healthy young adults (total N = 405). Three experiments yielded a surprising nonlinear relationship between the proportion of pair-wise connected objects and capacity, with the highest capacity observed for homogenous displays, when either all objects were connected or disjointed. A drop in capacity, ranging from an average of a quarter of (...) an object out of three objects maintained in VWM, was noted when only some objects were connected while others were disjointed. As indicated by another two experiments, this effect was specific to double-feature encoding, but disappeared when single visual features had to be memorized. No existing theoretical model of VWM can directly explain this novel effect. Overall, the nonlinear effect of spatial connectedness implies that representations in VWM possess hierarchical structure defined by wholes, parts, features, and their relations, and the heterogeneity of such a structure hinders VWM performance, while homogeneity facilitates it. (shrink)