Principle For Dynamical Systems Research Articles

Maximal large deviations and slow recurrences in weakly chaotic systems

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

Corrigendum

System Dynamics ReviewVolume 38, Issue 4 p. 419-419 CorrigendumFree Access Corrigendum This article corrects the following: Fons et origo: reflections on the 60th anniversary of Industrial Dynamics David C. Lane, Volume 38Issue 3System Dynamics Review pages: 292-324 First Published online: October 5, 2022 First published: 07 November 2022 https://doi.org/10.1002/sdr.1722AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Syst. Dyn. Rev. 38, 317, 319–321 (2022). In the paper by David C. Lane (2022), the following references have been corrected: Burrell and Morgan, 1979 From: … 1985th ed. Aldershot: Gower. To: … 1985 ed. Aldershot: Gower. Henize, 1970 From: ‘Principles of Dynamics Systems’ To: ‘Principles of Dynamic Systems’ Malczynski and Lane, 2023 From: … System Dynamics Review 39(1) To appear. To: … System Dynamics Review. http://doi.org/10.1002/sdr.1720. Rand, 2003 From: International MIT System Dynamics Group Literature Collection Transactions in Operational Research … To: International Transactions in Operational Research … REFERENCE Lane DC. 2022. Fons et origo: reflections on the 60th anniversary of Industrial Dynamics. System Dynamics 38(3): 292– 324. Volume38, Issue4October/December 2022Pages 419-419 ReferencesRelatedInformation

New Directions in the Conceptualization and Assessment of Personality—A Dynamic Systems Approach

In this paper, we demonstrate how an integrative approach to personality—one that combines within–person and between–person differences—can be achieved by drawing on the principles of dynamic systems theory. The dynamic systems perspective has the potential to reconcile both the stable and dynamic aspect of personality, it allows including different levels of analysis (i.e. traits and states), and it can account for regulatory mechanisms, as well as dynamic interactions between the elements of the system, and changes over time. While all of these features are obviously appealing, implementing a dynamic systems approach to personality is challenging. It requires new conceptual models, specific longitudinal research designs, and complex data analytical methods. In response to these issues, the first part of our paper discusses the Personality Dynamics model, a model that integrates the dynamic systems principles in a relatively straightforward way. Second, we review associated methodological and statistical tools that allow empirically testing the PersDyn model. Finally, the model and associated methodological and statistical tools are illustrated using an experience sampling methodology data set measuring Big Five personality states in 59 participants ( N = 1916 repeated measurements). © 2020 The Authors. European Journal of Personality published by John Wiley & Sons Ltd on behalf of European Association of Personality Psychology

Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations.

The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian Lévy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian formalism under the Lévy fluctuations with exponentially light jumps for one- and two-dimensional stochastic dynamical systems. This formalism is based on a recently proved large deviation principle for dynamical systems under non-Gaussian Lévy perturbations. We demonstrate how to compute the most probable exit path and the quasi-potential by several examples. Meanwhile, we explore the impacts of the jump measure on the quasi-potential quantitatively and on the most probable exit path qualitatively. Results show that the quasi-potential can be well estimated by an approximate analytical expression. Moreover, we discover that although the most probable exit paths are analogous to the Gaussian case for the isotropic noise, the anisotropic noise leads to significant changes in the structure of the exit paths. These findings shed light on the underlying qualitative mechanism and quantitative feature of the exit phenomenon induced by non-Gaussian noise.

Large deviation principle for dynamical systems coupled with diffusion–transmutation processes

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process — where the latter jumps from one mode to another, and thus modifying the dynamics of the system. In particular, we study the exit problem, i.e., an asymptotic estimate for the exit probabilities with which the corresponding processes exit from a given bounded open domain, and then formally prove a large deviation principle for the exit position joint with the type occupation times as the random perturbation vanishes. Moreover, under certain conditions, we also determine the exit place and the type of distribution at the exit time and, as a consequence of this, such information also give the limit of the Dirichlet problem for the corresponding partial differential equation systems with a vanishing small parameter.

Design and FPGA-Based Realization of a Chaotic Secure Video Communication System

This paper initiates a systematic methodology for real-time chaos-based video encryption and decryption communications on the system design and algorithm analysis. The proposed system design and algorithm analysis have been validated on an FPGA hardware platform via Verilog Hardware Description Language (Verilog HDL). Based on the fundamental anti-control principles of dynamical systems, a 6-D real domain chaotic system is designed, and then the corresponding Verilog HDL algorithm is developed. The proposed Verilog HDL algorithm is utilized to design a real-time chaos-based secure video communication system, with a generalized design principle derived, which is implemented on an FPGA hardware platform equipped with an XUP Virtex-II chip. Following this line, the designed working mechanism is demonstrated by hardware experiments. The security performance is tested using the TESTU01 statistical test suites, the differential analysis, and the sensitivity of key parameters mismatch. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed system.

Rates in Almost Sure Invariance Principle for Dynamical Systems with Some Hyperbolicity

We prove the almost sure invariance principle with rate $${o(n^{\varepsilon})}$$ for every $${\varepsilon > 0}$$ for Hölder continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails. Examples include Gibbs–Markov maps with big images, Axiom A diffeomorphisms, dispersing billiards and a class of logistic and Hénon maps. The best previously proved rate is $${O(n^{1/4} (\log n)^{1/2} (\log \log n)^{1/4})}$$ . As a part of our method, we show that nonuniformly expanding transformations are factors of Markov shifts with simple structure and natural metric (similar to the classical Young towers). The factor map is Lipschitz continuous and probability measure preserving. For this we do not require the exponential tails.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Introduction to Focus Issue: Complex network perspectives on flow systems.

During the last few years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of dynamical systems from a variety of different fields. Among others, recent successful examples include (i) functional (correlation) network approaches to infer hidden statistical interrelationships between macroscopic regions of the human brain or the Earth's climate system, (ii) Lagrangian flow networks allowing to trace dynamically relevant fluid-flow structures in atmosphere, ocean or, more general, the phase space of complex systems, and (iii) time series networks unveiling fundamental organization principles of dynamical systems. In this spirit, complex network approaches have proven useful for data-driven learning of dynamical processes (like those acting within and between sub-components of the Earth's climate system) that are hidden to other analysis techniques. This Focus Issue presents a collection of contributions addressing the description of flows and associated transport processes from the network point of view and its relationship to other approaches which deal with fluid transport and mixing and/or use complex network techniques.

Optimal principle for dynamical system with alterative orbiting

Lagrange problem with the account of functional limitation at any functional limitations atany moment in a given interval is presented. The required conditions for optimal trajectories of thedeterminated dynamic system synthesized as space vehicle trajectories have been obtained

Toward Integrative Dynamic Models for Adaptive Perspective Taking.

In a matter of mere milliseconds, conversational partners can transform their expectations about the world in a way that accords with another person's perspective. At the same time, in similar situations, the exact opposite also appears to be true. Rather than being at odds, these findings suggest that there are multiple contextual and processing constraints that may guide when and how people consider perspective. These constraints are shaped by a host of factors, including the availability of social and environmental cues, and intrinsic biases and cognitive abilities. To explain how these might be integrated in a new way forward, we turn to an adaptive account of interpersonal interaction. This account draws from basic principles of dynamical systems, principles that we argue are already expressed, both implicitly and explicitly, within a broad landscape of existing research. We then showcase an initial attempt to develop a computational framework to instantiate some of these principles. This framework, consisting of what we argue to be important mechanistic insights rendered by neural network models, is based on a promising and long-standing approach that has yet to take hold in the current domain. We argue that by bridging this gap, new insights into other theoretical accounts, such as the connections between memory and common ground information, might be revealed.

The dynamics of emotions in online interaction.

We study the changes in emotional states induced by reading and participating in online discussions, empirically testing a computational model of online emotional interaction. Using principles of dynamical systems, we quantify changes in valence and arousal through subjective reports, as recorded in three independent studies including 207 participants (110 female). In the context of online discussions, the dynamics of valence and arousal is composed of two forces: an internal relaxation towards baseline values independent of the emotional charge of the discussion and a driving force of emotional states that depends on the content of the discussion. The dynamics of valence show the existence of positive and negative tendencies, while arousal increases when reading emotional content regardless of its polarity. The tendency of participants to take part in the discussion increases with positive arousal. When participating in an online discussion, the content of participants' expression depends on their valence, and their arousal significantly decreases afterwards as a regulation mechanism. We illustrate how these results allow the design of agent-based models to reproduce and analyse emotions in online communities. Our work empirically validates the microdynamics of a model of online collective emotions, bridging online data analysis with research in the laboratory.

Unmasking the soil cover's disruption by use of a dynamic model of measurement aerospace parameters of ground vegetation

The "Introduction" describes topicality and importance of revealing the soil cover's disruption for a wide range of fields. It was shown that spectral brightness and colorimetric parameters of ground vegetation can be used for this task. However, a traditional scheme of data processing for remote sensing requires a long-term observations and can not always be applied, if quick decision-making is necessary or there is lack of information. Such cases require the use of special methods, one of which is a dynamic model developed with authors' participation based on the following basic relationships: (+,-) (-, -) (+, 0), (-, 0) (0,0). The section "Brief description of a dynamic model" describes the basic principles of dynamic systems used to solve the problem. Using above-mentioned relationships, the dynamics of a system consisting of several components is constructed and its main properties are listed. The main feature of this model is that the identification of structure and parameters of the dynamic system does not required sequential order of observations (as for models based on time series). This feature of the model enables for identifying the system's parameters of dynamics of the natural system to use information from a single picture taken from the spacecraft rather than long-term observations. The section "Materials and Methods" describes specific colorimetric parameters used to analyze the vegetation cover. The section "Obtained results" contains an example of the model's application to a satellite image for detecting the differences in two sites of a field with vegetation. One site is a recultivated area near the liquidated gas-oil well, another site is non-recultivated area at a considerable distance from the well (500-1000 m). The simulation results are described by eight signed graphs (4 graphs for each sites), whose structure allows to identify the system differences between the two cases. The section "Conclusions" summarizes the results of previous sections. The prospects of the use of proposed methodology for soil cover's disruption are shown. Advantages of this methodology over other approaches are highlighted.

Развитие идей саморегуляции в исторической ретроспективе

Psychology of self-regulation is a relatively new but rapidly developing branch of psychological science. It has integrated many of the ideas that were initially born within the framework of physiology and cybernet¬ics. Interpretations of mechanisms underlying self-regulation are closely related to the general principles of dynamic systems' functioning on the basis of feedback. These principles were defined in the works of the Russian physiologists N.A. Bernstein and P.K. Anokhin and in the cybernetic models of Western scientists. Ideas of L.S. Vygotsky, S.L. Rubinstein, A.N. Leontiev, P. Janet, J. Piaget and others have also had a significant impact on the development of modern concepts of self-regulation. The paper provides a historical insight into the origins of ideas of self-regulation and shows how they have evolved from the concept of self-regulation as adaptation to the concepts of reasonable changes, subjective activity, conscious self-regulation, self-determi¬nation and self-efficacy, and individual styles of self-regulation.

Stochastic averaging principle for dynamical systems with fractional Brownian motion

Stochastic averaging for a class of stochastic differentialequations (SDEs) with fractional Brownian motion, of the Hurst parameter $H$ inthe interval $(\frac{1}{2},1)$, is investigated. An averaged SDE for theoriginal SDE is proposed, and their solutions are quantitatively compared. Itis shown that the solution of the averaged SDE converges to that of theoriginal SDE in the sense of mean square and also in probability. It is furtherdemonstrated that a similar averaging principle holds for SDEs understochastic integral of pathwise backward and forward types. Two examples arepresented and numerical simulations are carriedout to illustrate the averaging principle.

Extended framework of Hamilton’s principle for continuum dynamics

Hamilton’s principle is the variational principle for dynamical systems, and it has been widely used in mathematical physics and engineering. However, it has a critical weakness, termed end-point constraints, which means that in the weak form, we cannot use the given initial conditions properly. By utilizing a mixed formulation and sequentially assigning initial conditions, this paper presents a novel extended framework of Hamilton’s principle for continuum dynamics, to resolve such weakness. The primary applications lie in an elastic and a J2-viscoplastic continuum dynamics. The framework is simple, and initiates the development of a space–time finite element method with the proper use of initial conditions. Non-iterative numerical algorithms for both elasticity and J2-viscoplasticity are presented.

Effects of cognitive style on digital jigsaw puzzle performance: A GridWare analysis

Cognitive style, a personal characteristic that is a combination of cognitive controls such as field independence (FI) and field dependence (FD), may influence game performance. FI and FD were measured in 210 5th-grade students using a Group Embedded Figures Test. Students assembled digital jigsaw puzzles based on maps of Taiwan and Europe. Using principles of dynamic systems, game performance was analyzed using GridWare, and four types of game strategy were identified. The results showed that cognitive style, based on FI and the number of events, was able to predict digital jigsaw puzzle scores. Digital jigsaw puzzle scoring was positively correlated with FI. FI students achieved significantly higher scores than FD students. Practical implications and limitations were discussed.

Almost sure invariance principle for dynamical systems by spectral methods

We prove the almost sure invariance principle for stationary R^d--valued processes (with dimension-independent very precise error terms), solely under a strong assumption on the characteristic functions of these processes. This assumption is easy to check for large classes of dynamical systems or Markov chains, using strong or weak spectral perturbation arguments.

Emergence and the Analytic Third: Working at the Edge of Chaos

This paper provides an integration of dynamic systems principles with the concept of the Analytic Third to further understand the therapeutic properties of the alliance between analyst and patient. I argue that the Analytic Third is an emergent phenomenon, in which something that is more than the sum of its parts is created, leading to an expansion of the capacity for play and spontaneity—with words, in relating to others, within the metaphor of the transference—which is one of the essential elements of therapeutic action. Rupture and repair is the central movement of therapeutic action, with mutual understanding building both mutual recognition and a stronger self-object bond. Adolescents can perhaps offer us the most striking and dramatic illustrations of emergence, because their analyses are particularly likely to unfold chaotically, often rapidly oscillating between periods of introspection and nonreflective action, but eventually shifting toward adaptation. A series of clinical vignettes taken from the analysis of an adolescent boy are utilized to illustrate these principles.

Discussion of Dr. Judy Pickles's Paper: The Perspective of Nonlinear Open Systems Theory

Nonlinear dynamic systems theory originally began as an attempt to understand interactions in both living and nonliving systems such as ecosystems and cloud formations. Because it is a field and systems theory, dynamic systems concepts offer a rich source of patented applications to the psychoanalytic situation. This article first briefly reviews some basic dynamic systems principles. The clinical material presented by Dr. Pickles is then discussed with an effort to apply dynamic systems concepts. In particular, the notions of introducing novelty and the need for measured perturbation as part of the process of analytic change are emphasized.