WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE SERIES B – serie

This book comprises the most recent advanced results on nonlinear electronic circuits, and the contents range from networks, synchronization, memristors to several other topics. Both theory and advanced timely results are included. It provides an overview of popular themes in the field of nonlinear dynamics of electronic circuits with contributions from outstanding scientists.

What is synchronization? This book will show how the concept of closeness of states or frequencies between two dynamical systems has evolved from synchronization to consensus. Part 1 introduces the concepts and mathematical descriptions of Generalized Synchronization (GS) while Part 2 covers Generalized Consensus (GC).It is suitable for researchers and practitioners undertaking the studies of synchronization and consensus of multi-agent systems, graduate students and senior undergraduate students with the backgrounds in calculus, linear algebra and ordinary differential equations, equipped with computer programming skills, in mathematics, physics, engineering and even social sciences.

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.

Understanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.

The papers in this edited volume aim to provide a better understanding of the dynamics and control of a large class of hybrid dynamical systems that are described by different models in different state space domains. They not only cover important aspects and tools for hybrid systems analysis and control, but also a number of experimental realizations. Special attention is given to synchronization — a universal phenomenon in nonlinear science that gained tremendous significance since its discovery by Huygens in the 17th century. Possible applications of the results introduced in the book include control of mobile robots, control of CD/DVD players, flexible manufacturing lines, and complex networks of interacting agents.The book is based on the material presented at a similarly entitled minisymposium at the 6th European Nonlinear Dynamics Conference held in St Petersburg in 2008. It is unique in that it contains results of several international and interdisciplinary collaborations in the field, and reflects state-of-the-art technological development in the area of hybrid mechanical systems at the forefront of the 21st century.

The book is a compilation of selected papers from the conference on Physics and Control 2009, presenting a unified perspective underlying the thematics and strategies related to the control of physical systems with emerging applications in physics, engineering, chemistry, biology and other natural sciences. The selected papers reflect the state-of-the-art of the more advanced theoretical and practical studies in the field of control of complex systems. The contributions provide a comprehensive view on some selected topics of particular importance at the disciplinary borderline between Physics and Control.

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

This book is to celebrate the contributions of Professor Joaquín Álvarez Gallegos, a pioneer in the promotion and development of dynamical systems, control and synchronization in the Mexican community. The book presents a collection of original research contributions addressing recent theoretical advances and authoritative state-of-the-art reviews on topics related to the field of Dynamics, Control and Synchronization. The chapters contained in the book are written by international experts, who have collaborated in some way with Professor Álvarez, including former MSc- and PhD students. The book will be organized in three parts, one focusing on the analysis of complex nonlinear dynamics, including chaotic dynamics, whereas the second part is devoted to synchronization of interconnected complex systems. The final part of the book is dedicated to the control of nonlinear systems, in particular, to the design and implementation of robust control techniques, and its potential application in mechanical systems. Here typically connections with the other parts will be included and where possible illustrated by real examples. This book is suitable for scientists, control engineers and dynamicists interested in a timely review related to the control of nonlinear systems and how this intersects to the modelling, analysis and synchronization of complex systems.

This invaluable compilation on the 35th anniversary of the well-established journal International Journal of Bifurcation and Chaos, published as a special issue in November 2025, is a collection of 12 chapters written by renowned and leading researchers in the fields of memristors, nonlinear dynamics and complexity. A broad range of topics covered include memristors, bifurcations, chaos, complex power grids and nonlinear network dynamics, with surveys and overviews of technical developments in the fields.

For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme simplicity and robustness has made it the circuit of choice for generating chaotic signals for practical applications.In addition to the 48 illuminating papers drawn from a recent two-part Special Issue (March and June, 1993) of the Journal of Circuits, Systems, and Computers devoted exclusively to Chua's circuit, several highly illustrative tutorials and incisive state-of-the-art reviews on the latest experimental, computational, and analytical investigations on chaos are also included. To enhance its pedagogical value, a diskette containing a user-friendly software and data base on many basic chaotic phenomena is attached to the book, as well as a gallery of stunningly colorful strange attractors.Beginning with an elementary (freshman-level physics) introduction on experimental chaos, the book presents a step-by-step guided tour, with papers of increasing complexity, which covers almost every conceivable aspects of bifurcation and chaos. The second half of the book contains many original materials contributed by world-renowned authorities on chaos, including L P Shil'nikov, A N Sharkovsky, M Misiurewicz, A I Mees, R Lozi, L O Chua and V S Afraimovich.The scope of topics covered is quite comprehensive, including at least one paper on each of the following topics: routes to chaos, 1-D maps, universality, self-similarity, 2-parameter renormalization group analysis, piecewise-linear dynamics, slow-fast dynamics, confinor analysis, symmetry breaking, strange attractors, basins of attraction, geometric invariants, time-series reconstruction, Lyapunov exponents, bispectral analysis, homoclinic bifurcation, stochastic resonance, synchronization, and control of chaos, as well as several novel applications of chaos, including secure communications, visual sensing, neural networks, dry turbulence, nonlinear waves and music.

The papers in this volume summarizes the state-of-the-art in the use of concepts of dynamical systems theory to study chaotic evolution and spatiotemporal complexity.The central results of dynamical systems theory have demonstrated that simple deterministic mathematical systems can produce highly disordered dynamical behaviour, suggesting that it might be possible to explain complex natural phenomena with relatively simple models. This proved to be far more difficult than had been initially anticipated. It is increasingly clear that the naive application of dynamical methods can readily produce spurions indications of deterministic behavior. Many dynamicists are currently preoccupied with the development of methods that can bring increased rigor and reliability to the anlaysis of experimental data. At the same time, techniques have been developed for controlling the behavior of complex systems, for predicting their evolution, and for describing their behavior even when this behavior displays complexity in space as well as in time. The papers in this collection dicuss techniques used to confirm the existence of chaotic behavior by means of surrogate data, topological information and quantitative measures of determinism, techniques for controlling and predicting chaotic behavior, and illustrations of the use of these techniques in laser physics, acoustics, hydrodynamics, oceanography, climatology, biology, medicine and economics.

This text, intended to be of use to fluid physicists, covers topics including: statistical mechanical treatment of inhomogeneous fluids; foam stability; dynamics of vortices; internal solitary waves in stratified shear flows; and evidence for solitary waves in Marangoni-Benard convection.

This volume contains a selection of papers presented at Euromech Colloquium 308 — Chaos and Noise in Dynamical Systems.Roughly speaking, a chaotic solution to an ordinary differential equation is aperiodic and “looks like” a stochastic process. On the other hand, the theory of probability and stochastic processes was developed to describe complicated irregular phenomena taking place in the real world, which in most cases are chaotic. This observation led to the idea of bringing together experts on both nonlinear chaotic and stochastic systems for the conference. Equal attention was given to recent theoretical results and practical applications.The revised and updated papers in this volume are grouped in the following sections: Theory of Chaotic Systems; Stochastic Systems; Spatiotemporal Systems and Fluid Dynamics; Numerical Tools; and Practical Applications. Each section starts with a short introduction and a brief summary of the presented papers.

This text contains the proceedings of two conferences on chaos in mesoscopic systems. The study of chaos in quantum systems has led to an understanding of quantum billiards and to the statistics of the distribution of energy levels of those systems.

This volume gives an overview of the recent ideas in studies of nonlinear waves and pattern formation in physical, chemical and biological active media.The papers deal with spatio-temporal growth of bacterial colonies, pattern formation and pattern recognition, pattern selection in Bénard–Marangoni convection, chemical turbulence and parametric resonance of vortices in the Belousov–Zhabotinsky reaction, oscillatory electrodissolution of metals, discretely-coupled electronic arrays, optical space-time complexity, spiral waves in nematic liquid crystals and several approaches to control chaos. The stability of hexagonal patterns with some asymmetries are analyzed, both for convective systems and Turing structures. Some other lectures are devoted to the important question of the topology of defects in superfluids, convective and reaction-diffusion systems.

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 introduced via concrete examples. A common feature is that most of the systems under study are extended, nonhomogeneous and far from equilibrium. The book also exhibits an interesting interplay between deterministic and stochastic approaches.

These proceedings contain a collection of papers on Combinatorial Dynamics, from the lectures that took place during the international symposium, Thirty Years after Sharkovskiĭ's Theorem: New Perspectives, which was held at La Manga del Mar Menor, Murcia, Spain, from June 13 to June 18, 1994.Since Professor A N Sharkovskiĭ's landmark paper on the coexistence of periods for interval maps, several lines of research have been developed, opening applications of models to help understand a number of phenomena from a wide variety of fields, such as biology, economics, physics, etc. The meeting served to summarize the progress made since Professor Sharkovskiĭ's discovery, and to explore new directions.

This workshop brought together experts involved in different fields of discrete nonlinear dynamics to assess the recent developments in these areas. The participants studied intensively the subjects in areas which could in principle be regarded as different points of view: cardiology, electronics, biophysics, chemistry, etc. The subjects covered focused on the common biophysical problems related to the discrete nature of the different systems considered. Systems of discretely-coupled dynamical systems often serve as standard models for investigating the phenomena occuring in transformation and transport processes in living cells, tissues, neuronal networks, physiological systems and ecosystems, as well as in all forms of chemical, biochemical and biological reactors and combustion systems. Biological systems are discrete by their very nature: ensembles of cardiac cells, bacteria, ants, slime mold cells, etc. It is remarkable that such discrete systems may behave — in a macroscopic scale — differently to the corresponding continuous models.

This book presents a unified picture of recent progress in diverse interdisciplinary problems of nonlinear dynamics and chaos. The major topics covered include waves, patterns and instabilities in spatially extended systems, coupled oscillations and neuronal systems, granular dynamics and complex systems, chaos control, and applications of chaos and nonlinear dynamics. The book will give researchers and graduate students interested in nonlinear dynamics a pointer on the future direction of this rapidly developing field.

In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.