Chaotic Systems With Multistability And Hidden Attractors

Download or read book Chaotic Systems with Multistability and Hidden Attractors written by Xiong Wang and published by Springer Nature. This book was released on 2021-12-01 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.

Download or read book Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors written by Christos Volos and published by MDPI. This book was released on 2019-05-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Recent Trends In Chaotic, Nonlinear And Complex Dynamics written by Jan Awrejcewicz and published by World Scientific. This book was released on 2021-07-26 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Systems with Hidden Attractors written by Viet-Thanh Pham and published by Springer. This book was released on 2017-03-10 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors written by Viet-Thanh Pham and published by Springer. This book was released on 2018-02-26 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Strange Nonchaotic Attractors written by Ulrike Feudel and published by World Scientific. This book was released on 2006 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed. Key Features Topics are suitable for various disciplines dealing with nonlinear dynamics (mechanics, physics, nonlinear optics, hydrodynamics, chemical kinetics, etc.) A variety of theoretical tools is supplied to reveal different characteristics of strange nonchaotic behavior Readership: Graduate students and researchers in nonlinear science.

Download or read book A Gallery of Chua Attractors written by Eleonora Bilotta and published by World Scientific. This book was released on 2008 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).