Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science.

Topics in Nonlinear Dynamics, Volume 3, Proceedings of the 30th IMAC, A Conference and Exposition on Structural Dynamics, 2012, the third volume of six from the Conference, brings together 26 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Application of Nonlinearities: Aerospace Structures Nonlinear Dynamics Effects Under Shock Loading Application of Nonlinearities: Vibration Reduction Nonlinear Dynamics: Testing Nonlinear Dynamics: Simulation Nonlinear Dynamics: Identification Nonlinear Dynamics: Localization

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

Ch. 1. Generalized Hamiltonian systems / D. Cheng -- ch. 2. Continuous finite-time control / T. P. Leung and Y. Hong -- ch. 3. Local stabilization of nonlinear systems by dynamic output feedback / P. Chen and H. Qin -- ch. 4. Hybrid control for global stabilization of a class of systems / J. Zhao -- ch. 5. Robust and adaptive control of nonholonomic mechanical systems with applications to mobile robots / Y. M. Hu and W. Huo -- ch. 6. Introduction to chaos control and anti-control / G. Chen ... [et al.].

This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, nonlinear modal analysis and model reduction, synchronization, and strongly nonlinear dynamics. Interwoven seamlessly, these groups cover a wide range of topics, from fundamental concepts to practical applications, catering to both introductory and advanced readers. The first group, consisting of chapters 1 and 2, serves as an introduction to the theory of parametric resonance and the dynamics of parametrically excited slender structures. Chapters 3, 4, and 5 form the second group, offering insights into normal forms, nonlinear normal modes, and nonlinear system identification. Chapters 6 and 7 delve into asynchronous modes of structural vibration and master-slave topologies for time signal distribution within synchronous systems, respectively, representing the third group. Finally, the last four chapters tackle the fourth group, exploring nonlinear dynamics of variable mass oscillators, advanced analytical methods for strong nonlinear vibration problems, chaos theory, and dynamic integrity from the perspectives of safety and design. This book harmoniously combines theoretical depth and practical relevance to provide a comprehensive understanding of nonlinear dynamics.

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

This book focuses on the research topics investigated during the three-year research project funded by the Italian Ministero dell'Istruzione, dell'Universite e della Ricerca (MIUR: Ministry of Education, University and Research) under the FIRB project RBNE01CW3M. With the aim of introducing newer perspectives of the research on complexity, the final results of the project are presented after a general introduction to the subject. The book is intended to provide researchers, PhD students, and people involved in research projects in companies with the basic fundamentals of complex systems and the advanced project results recently obtained.

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.

This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.

In the early 1980s, the late luminary Tito Arecchi was the first to highlight the existence of chaos in a laser model. Since then, along with several colleagues, he developed many important lines of research in this field, such as generalized multistability, laser with injected signal, laser with delayed feedback and the worldwide accepted classification of lasers of A, B and C, depending on their typical relaxation rates. Later, chaos control and synchronization were investigated in lasers and other systems, providing innovative schemes. Very recently, in his last contribution to laser physics, the model of the laser with feedback demonstrating its universal features was revisited.This book aims to present the research activity of Prof. Arecchi and his colleagues in the domain of nonlinear dynamics of lasers, since his seminal works of 1982 till the latest. Also included is our last contribution on jerk dynamics of laser's minimal universal model and a brief history of the discovery of laser where the reader will discover or rediscover many anecdotes about it.