Nonlinear Dynamics And Chaos Advances And Perspectives

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.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

The book covers different subjects in the field of nonlinear dynamics, especially applications and investigation of chaos and chaotic systems in electrical engineering, information technology, communication engineering and mechanical engineering. This book is suitable as a textbook at the graduate or advanced undergraduate level and will appeal to postgraduate-level students and young researchers in different fields. This book provides technological advancement in nonlinear dynamics and chaos and explores the fields of communication, electric vehicles, power systems and rotational machines with centrifugal flyball governor system. An autonomous chaotic system is explored with real and complex state variables; their projective synchronisation is reported with application to secure communication. Secure communication is achieved using Masking-Modulation and Diffie-Hellman Key Exchange encryption techniques. Further, electric vehicles are the necessity of upcoming trends. To optimize the control performance of the permanent-magnet synchronous motor with different disturbances and uncertainties, a nonlinear control for the permanent-magnet synchronous motor using sliding-mode control is reported and Cascaded PI sliding mode control technique is explored to control the chaotic behaviour in electric vehicles. Chaos behaviour is explored in power systems and its control is presented using higher order sliding mode control. Comparative performances are analysed followed by control of chaos in the Rotational Machine with Centrifugal Flyball Governor system where chaos is controlled using recursive backstepping sliding mode control. All the simulations are carried out in the MATLAB environment and reveal successful achievement of the objectives. Researchers from academia and industry, who are working in the research areas Nonlinear Dynamical Systems & Chaos, Electrical Engineering, Computer Science Engineering, Information Technology, Communication Engineering and Mechanical Engineering may be principal audiences. Also, the book will be helpful for (i) graduate or advanced undergraduate level students as a textbook or major reference book for courses such as electrical circuits, nonlinear dynamical systems, mathematical modelling, computational science, numerical simulation, and many others and (ii) postgraduate level students and young researchers in the following fields: Communication Engineering; Computer Science; Electrical and Electronic Engineering; Mechanical Engineering; Engineering Mathematics; Computational Physics.

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.

The goal of this Third Edition is the same as previous editions: to provide a good foundation - and a joyful experience - for anyone who'd like to learn about nonlinear dynamics and chaos from an applied perspective.

"The book covers different subjects in the field of nonlinear dynamics, especially applications and investigation of chaos and chaotic systems in electrical engineering, information technology, communication engineering and mechanical engineering. This book is suitable as a textbook at the graduate or advanced undergraduate level and will appeal to postgraduate-level students and young researchers in different fields. This book provides technological advancement in nonlinear dynamics and chaos and explores the fields of communication, electric vehicles, power systems and rotational machines with centrifugal flyball governor system. An autonomous chaotic system is explored with real and complex state variables; their projective synchronisation is reported with application to secure communication. Secure communication is achieved using Masking-Modulation and Diffie-Hellman Key Exchange encryption techniques. Further, electric vehicles are the necessity of upcoming trends. To optimize the control performance of the permanent-magnet synchronous motor with different disturbances and uncertainties, a nonlinear control for the permanent-magnet synchronous motor using sliding-mode control is reported and Cascaded PI sliding mode control technique is explored to control the chaotic behaviour in electric vehicles. Chaos behaviour is explored in power systems and its control is presented using higher order sliding mode control. Comparative performances are analysed followed by control of chaos in the Rotational Machine with Centrifugal Flyball Governor system where chaos is controlled using recursive backstepping sliding mode control. All the simulations are carried out in the MATLAB environment and reveal successful achievement of the objectives. Researchers from academia and industry, who are working in the research areas Nonlinear Dynamical Systems & Chaos, Electrical Engineering, Computer Science Engineering, Information Technology, Communication Engineering and Mechanical Engineering may be principal audiences. Also, the book will be helpful for (i) graduate or advanced undergraduate level students as a textbook or major reference book for courses such as electrical circuits, nonlinear dynamical systems, mathematical modelling, computational science, numerical simulation, and many others and (ii) postgraduate level students and young researchers in the following fields: Communication Engineering; Computer Science; Electrical and Electronic Engineering; Mechanical Engineering; Engineering Mathematics; Computational Physics"--

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys