Recent Advances In Nonlinear Dynamics And Synchronization

This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis of complex nonlinear dynamical systems. As such it addresses key challenges are addressed, e.g. efficient handling of time-varying dynamics, efficient design, faster numerical computations, robustness, stability and convergence of algorithms. The book provides a series of contributions discussing either the design or analysis of complex systems in sciences and engineering, and the concepts developed involve nonlinear dynamics, synchronization, optimization, machine learning, and forecasting. Both theoretical and practical aspects of diverse areas are investigated, specifically neurocomputing, transportation engineering, theoretical electrical engineering, signal processing, communications engineering, and computational intelligence. It is a valuable resource for students and researchers interested in nonlinear dynamics and synchronization with applications in selected areas.

After the first time chaos could be controlled, for the last quarter of century, a diversity of publications have been devoted to the development of new control schemes and their applications to different laser systems. This book assembles several review papers which analyze and describe the most important achievements in controlling laser dynamics and synchronization of laser systems. The papers report a variety of interesting dynamical phenomena encountered in different types of lasers and related to control techniques. For the last 20 years laser physics and nonlinear dynamics have undergone a crucial progress. Understanding lasers as dynamical systems involves concepts associated mostly with the nonlinear nature of these systems. Since the appearance of the pioneering work of E. Ott, C. Grebogi and J. A. Yorke in 1990, who proposed a method for controlling chaos, active attempts for applying this method and other control methods to laser systems have been conducted. Many research works were directed not only to the observation and identification of dynamical regimes in lasers, but also to control laser dynamics and chaos. Considerable progress has been made in research and development of semiconductor and fiber lasers. The special interest these lasers stir up is explained by their easy operation, small size, low price, and, of course, their successful application in communications. However, in spite of the huge progress in laser physics and nonlinear dynamics, only few reviews have been devoted to this topic. The book has an interdisciplinary character because the topic of this book is a great mixture of four big areas of science: laser physics, nonlinear dynamics, control theory, and synchronization. Each area was developed independently till the first nonlinear control of laser dynamics has been realized. The aim of this book is to address a broad readership: students, researchers, engineers, technicians, who work with lasers, as well as scientists conducting interdisciplinary research; it is intended for both theoreticians and experimentalists. The intention of this book is to give the reader a good understanding of nonlinear laser dynamics, not only in one specific type of laser but rather in many different types of lasers, as each control method or coupling is introduced. Four chapters of the book are devoted to laser dynamics control and describe the most important achievements of the last two decades in this topic. These chapters review already classical and relatively new results on stabilizing unstable periodic orbits in chaotic lasers and other control methods providing the reader with an extensive bibliography. The book also contains four chapters devoted to synchronization of coupled lasers. Special attention in the book is given to experimental applications of different control methods and synchronization phenomena in different laser systems. Editing this book has been a rewarding experience for me. Since 1979, I have been associated with lasers, beginning as a postgraduate student at the Institute of Physics of the Belarus Academy of Sciences in Minsk when I helped build a CO2 laser for a research project under Professor Vladimir V. Churakov direction. He was the first person to instil in me an enthusiasm for optics and light. I then was very fortunate to do my thesis work under supervision of Academician of the Byelorussian Academy of Sciences Boris Ivanovich Stepanov, who encouraged me to reduce ideas to simple concepts. Being very diligent, he nonetheless, also was a cheery person. He used to say that a real scientist has to work more than 24 hours per day, write monographs and must never stay too much time in one research area, but should change direction from time to time. I also thank Dr. Boris F. Kuntsevich for helping me to understand the fundamental theory of laser oscillations. At that time, in the late 70s - early 80s, since there were no personal computers we had to search for analytical solutions of laser equations. This was a good exercise to learn the foundation of laser physics. I am grateful to my colleagues Drs. Vladimir O. Petukhov and Ivan M. Bertel, who played a key role in my experimental practice helping me to install and equip my first experimental setup. Being a part of a stimulating group of young researchers at the Laboratory of General Spectroscopy during the growth of the field of laser spectroscopy was an unparalleled opportunity. We built CO2 lasers and tried to stabilize them for spectroscopy applications. For a long period of time Dr. Viacheslav N. Chizhevsky and I worked together, he got me involved in the world of chaos and helped me take my first steps into numerical simulations with MATLAB; together we carried out many experiments with CO2 lasers. He shared his ideas with me and I deeply appreciate all our fruitful discussions. Back then, we thought (about) laser was a stable device and treated any instabilities and chaos as a consequence of mechanical vibrations or bad alignment. It was only in 1964 that the Russian physicists A. Z. Grazyuk and A. N. Oraevskii found in numerical studies of the equations describing a simplest (homogeneously broadened, single-mode, traveling wave, resonantly tuned) laser, a time-dependent solution that consisted of pulses, varying irregularly with time. They even used at that time the term chaotic to describe this irregular pulsing behavior. Laser dynamics stagnated in a rudimentary state for more than one decade until in 1975, when the German theoretical physicist G. Haken concluded, from the isomorphy of a laser with Lorenz equations, that lasers could exhibit a non-periodic, pulsing emission, that is a chaotic emission. Even though, in the early 80s we did not believe that the Lorenz-Haken instability was inherent to real laser systems; thinking it was only an academic curiosity invented by theoreticians far removed from the daily reality of experimental laser physics, nonlinear laser dynamics was born and in 1982 after the first clear experimental evidence of laser chaos, was baptized by F. T. Arecchi These results, sharpening the perception of lasers as unstable systems, were then followed by a large number of experimental and theoretical investigations. Many researchers tried to exploit the new acquired knowledge of laser dynamics in some applications. Even though, the principal aim was still focused on avoiding instabilities to obtain a stable laser emission. Curiously, we had observed chaos in a bidirectional ring CO2 laser long before it was discovered by Prof. Arecchi's group. However, we did not pay serious attention to these findings, thinking it was the same chaotic behavior that had been previously observed in solid-state lasers. Moreover, we could not even publish our results in public scientific journals because in the Soviet Union of the 80's, during the period of Cold War, laser subjects were classified as top secret and not even the word laser was allowed to be used in open scientific literature. To evade this ban and get permission to publish our results, we had to replace the word laser by synonym words optical quantum generator . Many scientists who dealt with lasers were not allowed to go abroad and participate in international conferences. I was mainly a laser experimentalist until 1997, when I went to Canada with my own means to participate in the Summer School on Nonlinear Dynamics in Biology and Medicine organized by Leon Glass and Michael C. Mackey at McGill University in Montreal, where we took very useful lectures and practical exercises on theoretical modeling of physiological systems. Thanks to these lectures I came to realize that the world obeys universal dynamical laws, and also discovered for myself that many phenomena observed in lasers are present in a wide class of dynamical systems. This instilled in me the idea that a laser can serve as a very useful instrument to elaborate new methods for controlling nonlinear dynamics and chaos, which can be applied then to other systems, including biological and medical ones. Professor Arecchi and coworkers developed the same idea in their recent works; they do mention such similarity in the first chapter of this book. During the economically difficult period of the perestroika many scientists from the former Soviet Union had to abandon science and either go work for the industry or establish their own business. Some of the science-loving researchers who yet insisted on working at universities and research institutes had to paint roofs and towers or buy and resell things in order to survive. Many of us were looking for a job abroad. I was very fortunate to be invited first in 1992 by Professor Michel Herman from Physical Chemistry Laboratory at the University of Brussels where I spent three months working with dye lasers and fast Fourier spectroscopy. Then, thanks to Professor Ramón Corbalán who invited me to create the Laboratory of Infrared and Far Infrared Lasers at Universitat Autónoma de Barcelona, I spent almost seven years in Spain, where we carried out a series of interesting experiments on laser dynamics control. During that period I was happy to visit other universities and laser laboratories, such as the laboratory of Professor Pierre Glorieux at Université de Lille (France) and Professor Fortunato Tito Arecchi at Institute de Ottica Applicata in Florence (Italy), where we carried out several collaborative experiments with CO2 lasers. I also thank Professor Ari Olafson for the kind hospitality he extended to me in Reykjavik where I spent four unforgivable months in 1996 working at the University of Iceland. Finally, to round out my scientific carrier I was invited to Mexico in 1999 where I presently work as a Research Professor at Centro de Investigaciones en Optica in Leon, Guanajuato. I wish to thank Dr. Vicente Aboites, physicist and philosopher, for his kind invitation. Although the laser technology in Mexico is not yet advanced, the government is making a great effort to help develop national laser science and technology. I thank CONACYT (National Council for Science and Technology) for partial support of the publication of this book through project No. 46973-E, in particular, and research on lasers and applications, in general. Working in the field of lasers and nonlinear dynamics at several different institutions has provided me with a broad perspective that I hope has successfully contributed to the manner in which many of the concepts are presented in this book. I thank all of the authors who contributed to this book and to the reviewers who worked under great time pressure to complete the reviewing process in a relatively short time. I sincerely hope this book will stimulate new discussions and fundamental issues to a deeper level of understanding of laser dynamics and to develop new approaches to control and synchronization of laser systems. The results of this exercise could be also useful on the definition of scientific and technological programs related to this topic.

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

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.

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.

Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it offers an array of new, real-world applications in the field. Written by eminent scientists in the field of control theory and nonlinear systems from 19 countries (Cameroon, China, Ethiopia, France, Greece, India, Italia, Iran, Japan, Mexico, and more), this book covers the latest advances in chaos theory, along with the efficiency of novel synchronization approaches. Readers will find the fundamentals and algorithms related to the analysis and synchronization of chaotic systems, along with key applications, including electronic design, text and image encryption, and robot control and tracking. Explores and evaluates the latest real-world applications of chaos across various engineering and biomedical engineering fields Investigates advances in chaos synchronization techniques, including the continuous sliding-mode control approach, hybrid synchronization between chaotic and hyperchaotic systems, and neural network synchronization Presents recent advances in chaotic systems through an overview of new systems and new proprieties

Over the past years, the appropriateness of Computational Intelligence (CI) techniques in modeling and optimization tasks pertaining to complex nonlinear dynamic systems has become indubitable, as attested by a large number of studies reporting on the successful application of CI models in nonlinear science (for example, adaptive control, signal processing, medical diagnostic, pattern formation, living systems, etc.). This volume summarizes the state-of-the-art of CI in the context of nonlinear dynamic systems and synchronization. Aiming at fostering new breakthroughs, the chapters in the book focus on theoretical, experimental and computational aspects of recent advances in nonlinear science intertwined with computational intelligence techniques. In addition, all the chapters have a tutorial-oriented structure.