This volume focuses on the modeling of cognition, and brings together contributions from psychologists and researchers in the field of cognitive science. The shared platform of this work is to advocate a dynamical systems approach to cognition. Several aspects of this approach are considered here: chaos theory, artificial intelligence and Alfie models, catastrophe theory and, most importantly, self-organization theory or synergetics. The application of nonlinear systems theory to cognitive scien...
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the fre...
This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilist...
Written for the non-specialist scientist wishing to bring chaos theory into focus as something conceptually and operationally useful in scientific applications, this text bridges the gap between non-mathematical popular treatments and the distinctly mathematical publications that non-mathematicians find so difficult to penetrate. The book provides derivations or explanations of many key concepts, such as Kolmogorov-Sinai entropy, dimensions, Fourier analysis and Lyapunov exponents. Only basic al...
Interacting chaotic oscillators are of interest in many areas of physics, biology, and engineering. In the biological sciences, for instance, one of the challenging problems is to understand how a group of cells or functional units, each displaying complicated nonlinear dynamic phenomena, can interact with one another to produce a coherent response on a higher organizational level.This book is a guide to the fascinating new concept of chaotic synchronization. The topics covered range from transv...
This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.
Exploration Of A Nonlinear World: An Appreciation Of Howell Tong's Contributions To Statistics
This festschrift is dedicated to Professor Howell Tong on the occasion of his 65th birthday. With a Foreword written by Professor Peter Whittle, FRS, it celebrates Tong's path-breaking and tireless contributions to nonlinear time series analysis, chaos and statistics, by reprinting 10 selected papers by him and his collaborators, which are interleaved with 17 original reviews, written by 19 international experts.Through these papers and reviews, readers will have an opportunity to share many of...
Stability Of Gyroscopic Systems (Series On Stability, Vibration And Control Of Systems, Series A, #2)
The motion of mechanical systems undergoing rotation about a fixed axis has been the subject of extensive studies over a few centuries. These systems are generally subject to gyroscopic forces which are associated with coriolis accelerations or mass transport and render complex dynamics.The unifying theme among topics presented in this book is the gyroscopic nature of the system equations of motion. The book represents comprehensive and detailed reviews of the state of art in four diverse applic...
Chaos, Information Processing And Paradoxical Games: The Legacy Of John S Nicolis
This volume provides a self-contained survey of the mechanisms presiding information processing and communication. The main thesis is that chaos and complexity are the basic ingredients allowing systems composed of interesting subunits to generate and process information and communicate in a meaningful way. Emphasis is placed on communication in the form of games and on the related issue of decision making under conditions of uncertainty. Biological, cognitive, physical, engineering and societal...
Nonlinear Systems, Vol. 1 (Understanding Complex Systems)
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and...
Fuzzy Sets and Systems (Mathematics in Science and Engineering)
by Didier J DuBois
On Self-Organization (Springer Series in Synergetics, #61)
The thread of self-organization which is now recognized as permeating many dynamical transformations in diverse systems around us seems set to unleash a revolution as influential as that of Darwin in the last century. Darwin removed the 'originator' of a species; self-organization now seeks to remove the 'organizer' from an organism. Methods of nonlinear dynamics have played a crucial role in opening up this field and if these methods have a progenitor it is Henri Poi~care (1854 - 1912) whose fi...
Positive Transfer Operators And Decay Of Correlations (Advanced Series in Nonlinear Dynamics, #16)
by Viviane Baladi
Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions.This book, addressed to mathematicians and mathematica...
Buying Time For Climate Action: Exploring Ways Around Stumbling Blocks (Exploring Complexity, #0)
The 2021 IPCC report made one thing crystal clear - global climate change is here to stay. Time is up. We need to act or climate change will lead to inconceivable suffering by billions of people. Buying Time for Climate Action is the combined narrative of world class experts, all committed to help humanity survive its largely self-induced destructive course. Changing that course requires urgent action. Determining which actions will lead to helpful change requires insights into the stumbling blo...
Biological Systems: Nonlinear Dynamics Approach (SEMA SIMAI Springer, #20)
This book collects recent advances in the field of nonlinear dynamics in biological systems. Focusing on medical applications as well as more fundamental questions in biochemistry, it presents recent findings in areas such as control in chemically driven reaction-diffusion systems, electrical wave propagation through heart tissue, neural network growth, chiral symmetry breaking in polymers and mechanochemical pattern formation in the cytoplasm, particularly in the context of cardiac cells....
Non-linearity and Chaos in Engineering Dynamics
Presents the latest research of leading international groups in theoretical and applied dynamics. It starts with a general introduction to the basic concepts of nonlinear dynamics and chaos. Also includes topics on nonlinear problems of structural, mechanical, aerospace and naval engineering; topological and computer methods; cell mapping and global analysis; control of chaos; experimental studies; time series analysis and phase-space reconstruction.
Dynamics Of Nonlinear And Disordered Systems (World Scientific Series On Nonlinear Science Series B, #6)
This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment. It consists of two innovative introductory presentations on dynamical systems and fluid dynamics and six chapters on advanced research. A nontrivial interrelation between the different topics becomes apparent throughout the book as an indication of the underlying unity and genericity of nonlinear phenomena. There is a continuous emphasis on conceptual issues often i...
Dynamical Systems: A Collection Of Papers (Advanced Series in Nonlinear Dynamics, #1)
by Yakov Sinai
This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.
Smooth Invariant Manifolds And Normal Forms (World Scientific Series on Nonlinear Science Series A, #7)
by Alexander Kopanskii and Idel U Bronstein
This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results o...
This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures...
Psychophysics is by definition mappings between events in the environment and levels of human sensory responses. In this text the methods of nonlinear dynamics, employing trajectories developed for simpler sensory modelling, are extended to classes of problems which lie at the interface between sensation and perception. A diversity of topics for which extensive empirical evidence exists are reformulated by writing their dynamics in terms of complex trajectories put into coupled lattices and into...
Nonlinear Periodic Waves And Their Modulations: An Introductory Course
by Anatoly M Kamchatnov
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to t...
This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.
Dynamics Of Complex And Irregular Systems - Bielefeld Encounters In Mathematics And Physics Viii
The papers presented in this volume cover a number of different aspects of stochastic analysis, probability theory, quantum field theory, functional integration, ergodic theory, quantum theory, statistical modelling, random graph theory and percolation theory. The lectures also point out strong interactions between various fields: the fertility of the relations between probability theory and quantum theory and the intriguing and economical way of deriving the classical standard model by using no...