Generation Of Self-excited, Hidden And Non-self-excited Attractors In Piecewise Linear Systems: Some Recent Approaches PDF Download
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Author: Eric Campos Canton Publisher: World Scientific ISBN: 9811274134 Category : Science Languages : en Pages : 192
Book Description
What kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors.This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart.This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.
Author: Eric Campos Canton Publisher: World Scientific ISBN: 9811274134 Category : Science Languages : en Pages : 192
Book Description
What kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors.This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart.This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.
Author: Eric Campos Cantón Publisher: ISBN: 9789811274121 Category : Attractors (Mathematics) Languages : en Pages : 0
Book Description
"A textbook that presents the fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems"--
Author: Christos Volos Publisher: MDPI ISBN: 3038978981 Category : Technology & Engineering Languages : en Pages : 290
Book Description
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
Author: Viet-Thanh Pham Publisher: Springer ISBN: 3319712438 Category : Technology & Engineering Languages : en Pages : 497
Book Description
This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.
Author: Jan Awrejcewicz Publisher: World Scientific ISBN: 981122191X Category : Science Languages : en Pages : 561
Book Description
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
Author: Eleonora Bilotta Publisher: World Scientific ISBN: 9812790624 Category : Mathematics Languages : en Pages : 607
Book Description
Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) — a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce.This book aims to bridge the gap. A gallery of nearly 900 “chaotic attractors” — some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations — are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.The contents have also appeared in the International Journal of Bifurcation and Chaos (2007).
Author: Mario Bernardo Publisher: Springer Science & Business Media ISBN: 1846287081 Category : Mathematics Languages : en Pages : 497
Book Description
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Author: Viet-Thanh Pham Publisher: Springer ISBN: 3319537210 Category : Technology & Engineering Languages : en Pages : 111
Book Description
This brief provides a general overview of nonlinear systems that exhibit hidden-attractor behavior, a topic of interest in subjects as divers as physics, mechanics, electronics and secure communications. The brief is intended for readers who want to understand the concepts of the hidden attractor and hidden-attractor systems and to implement such systems experimentally using common electronic components. Emergent topics in circuit implementation of systems with hidden attractors are included. The brief serves as an up-to-date reference on an important research topic for undergraduate/graduate students, laboratory researchers and lecturers in various areas of engineering and physics.
Author: Eric Campos Canton
Author: Eric Campos Canton
Author: Walter Lacarbonara
Author: Eric Campos-Cantón
Author: Eric Campos Cantón
Author: Christos Volos
Author: Viet-Thanh Pham
Author: Jan Awrejcewicz
Author: Eleonora Bilotta
Author: Mario Bernardo
Author: Viet-Thanh Pham