Regularity And Complexity In Dynamical Systems

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 52,7 Mb
Release : 2013-07-12
Category : Mathematics
ISBN : 9781461415237

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Regularity and Complexity in Dynamical Systems by Albert C. J. Luo Pdf

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Author : Dimitri Volchenkov,Xavier Leoncini
Publisher : Springer
Page : 311 pages
File Size : 41,5 Mb
Release : 2017-06-24
Category : Technology & Engineering
ISBN : 9783319580623

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Regularity and Stochasticity of Nonlinear Dynamical Systems by Dimitri Volchenkov,Xavier Leoncini Pdf

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Author : Johan Dubbeldam,Kirk Green,Daan Lenstra
Publisher : John Wiley & Sons
Page : 261 pages
File Size : 46,6 Mb
Release : 2011-02-21
Category : Science
ISBN : 9783527409310

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The Complexity of Dynamical Systems by Johan Dubbeldam,Kirk Green,Daan Lenstra Pdf

Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.

Author : Claudius Gros
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 51,7 Mb
Release : 2010-09-24
Category : Science
ISBN : 9783642047060

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Complex and Adaptive Dynamical Systems by Claudius Gros Pdf

Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.

Author : Anonim
Publisher : Unknown
Page : 29 pages
File Size : 55,9 Mb
Release : 2012
Category : Differentiable dynamical systems
ISBN : OCLC:801767169

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Mathematics of Complexity and Dynamical Systems by Anonim Pdf

Author : Albert C. J. Luo
Publisher : Springer
Page : 310 pages
File Size : 49,5 Mb
Release : 2015-07-30
Category : Science
ISBN : 9783662472750

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Discretization and Implicit Mapping Dynamics by Albert C. J. Luo Pdf

This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.

Author : Paolo Castiglioni,Luca Faes,Gaetano Valenza
Publisher : MDPI
Page : 296 pages
File Size : 51,7 Mb
Release : 2021-03-02
Category : Mathematics
ISBN : 9783039433681

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Assessing Complexity in Physiological Systems through Biomedical Signals Analysis by Paolo Castiglioni,Luca Faes,Gaetano Valenza Pdf

Complexity is a ubiquitous phenomenon in physiology that allows living systems to adapt to external perturbations. Fractal structures, self-organization, nonlinearity, interactions at different scales, and interconnections among systems through anatomical and functional networks, may originate complexity. Biomedical signals from physiological systems may carry information about the system complexity useful to identify physiological states, monitor health, and predict pathological events. Therefore, complexity analysis of biomedical signals is a rapidly evolving field aimed at extracting information on the physiological systems. This book consists of 16 contributions from authors with a strong scientific background in biomedical signals analysis. It includes reviews on the state-of-the-art of complexity studies in specific medical applications, new methods to improve complexity quantifiers, and novel complexity analyses in physiological or clinical scenarios. It presents a wide spectrum of methods investigating the entropic properties, multifractal structure, self-organized criticality, and information dynamics of biomedical signals touching upon three physiological areas: the cardiovascular system, the central nervous system, the heart-brain interactions. The book is aimed at experienced researchers in signal analysis and presents the latest trends in the complexity methods in physiology and medicine with the hope of inspiring future works advancing this fascinating area of research.

Author : Albert C. J. Luo
Publisher : L& H Scientific Publishing
Page : 2 pages
File Size : 52,7 Mb
Release : 2012
Category : Chaotic behavior in systems
ISBN : 9781621550006

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Continuous Dynamical Systems by Albert C. J. Luo Pdf

Continuous dynamical systems is a unique book on chaos which can be analytically expressed rather than numerically simulated only, and provides a simple and concise view of a theory of stability and bifurcation in continuous dynamical systems for a better understanding of regularity and complexity in dynamical systems. Linear continuous systems with repeated eigenvalues are presented as an introduction. Higher-order singularity, stability and bifurcation in nonlinear continuous dynamical systems are systematically discussed. The analytical routes of periodic flows to chaos are discussed comprehensively. In addition, the book presents the analytical predictions of the global transversality of a flow to separatrix and nonlinear Hamiltonian chaos to determine the physical mechanism of chaos in nonlinear dynamical systems. This book is written as a textbook or reference book for university students, professors and researchers in applied mathematics, physics, mechanics, and control.

Author : José Amigó
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,8 Mb
Release : 2010-03-20
Category : Science
ISBN : 9783642040849

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Permutation Complexity in Dynamical Systems by José Amigó Pdf

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

Author : Hernán González-Aguilar,Edgardo Ugalde
Publisher : Springer
Page : 240 pages
File Size : 43,8 Mb
Release : 2015-02-10
Category : Technology & Engineering
ISBN : 9783319098647

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Nonlinear Dynamics New Directions by Hernán González-Aguilar,Edgardo Ugalde Pdf

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynamics in biological · Includes a study of self-organized regularity in long-range systems · Explains use of Levenstein's distance for measuring lexical evolution rates

Author : Klaus Mainzer
Publisher : World Scientific
Page : 448 pages
File Size : 40,7 Mb
Release : 2005
Category : Science
ISBN : 9789812561923

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Symmetry and Complexity by Klaus Mainzer Pdf

Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity.

Author : Marat Akhmet,Mehmet Onur Fen
Publisher : Springer
Page : 457 pages
File Size : 55,5 Mb
Release : 2015-08-13
Category : Science
ISBN : 9783662475003

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Replication of Chaos in Neural Networks, Economics and Physics by Marat Akhmet,Mehmet Onur Fen Pdf

This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.

Author : Valentin Afraimovich,Albert C. J. Luo,Xilin Fu
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 50,5 Mb
Release : 2013-11-22
Category : Technology & Engineering
ISBN : 9783319023533

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Nonlinear Dynamics and Complexity by Valentin Afraimovich,Albert C. J. Luo,Xilin Fu Pdf

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 40,9 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : Albert C J Luo
Publisher : L& H Scientific Publishing
Page : 54 pages
File Size : 52,5 Mb
Release : 2011-12-01
Category : Mathematics
ISBN : 8210379456XXX

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Discrete and Switching Dynamical Systems by Albert C J Luo Pdf

Discrete and Switching Dynamical Systems is a unique book about stability and its switching complexity in discrete dynamical systems, and provides a simple and concise view of the theory of stability and bifurcation in nonlinear discrete dynamical systems. Linear discrete systems with repeated eigenvalues are presented as an introduction. Higher-order singularity, stability and bifurcations in nonlinear discrete dynamical systems are presented. Several examples are presented to illustrate chaos fractality and complete dynamics of nonlinear discrete dynamical systems. Switching systems with transports are discussed comprehensively as a general fashion to present continuous and discrete mixed systems, and mapping dynamics, grazing phenomena and strange attractor fragmentation are also presented for a better understanding of regularity and complexity in discrete, switching and discontinuous dynamical systems. This book is written as a textbook or reference book for university students, professors and researchers in applied mathematics, physics, engineering, economics dynamics and finance. Albert C.J. Luo is an internationally recognized professor in nonlinear dynamics and mechanics. He worked at Southern Illinois University Edwardsville, USA. His principal research interests lie in the fields of Hamiltonian chaos, nonlinear mechanics, and discontinuous dynamical systems. A different view of stability and bifurcations in discrete dynamical systemsHigher order singularity, stability switching complexity and bifurcationsChaos fractality and complete dynamicsHow to construct mappings from physical systemsMapping dynamics, grazing invariance and strange attractor fragmentationUser friendly presentation and intuitive illustrationsWide audience due to instructive and comprehensive examples