The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. - Presents comprehensive theory and methodology of stability analysis - Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation - Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.

This volume reviews examples and notions of robustness at several levels of biological organization. It tackles many philosophical and conceptual issues and casts an outlook on the future challenges of robustness studies in the context of a practice-oriented philosophy of science. The focus of discussion is on concrete case studies. These highlight the necessity of a level-dependent description of robust biological behaviors.Experts from the neurosciences, biochemistry, ecology, biology, and the history and the philosophy of life sciences provide a multiplex perspective on the topic. Contributions span from protein folding, to cell-level robustness, to organismal and developmental robustness, to sensorimotor systems, up to the robustness of ecological systems.Several chapters detail neurobiological case-studies. The brain, the poster child of plasticity in biology, offers multiple examples of robustness. Neurobiology explores the importance of temporal organization and multiscalarity in making this robustness-with-plasticity possible. The discussion also includes structures well beyond the brain, such as muscles and the complex feedback loops involved in the peculiar robustness of music perception. Overall, the volume grounds general reflections upon concrete case studies, opening to all the life sciences but also to non-biological and bio-inspired fields such as post-modern engineering. It will appeal to researchers, students, as well as non-expert readers.

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

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.

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Offers an exposition of the central results of Differentiable Dynamics. This edition includes an Appendix reviewing the developments under five basic areas: nonlinear oscillations, diffeomorphisms and foliations, general theory; dissipative dynamics, general theory; conservative dynamics, and, chaos, catastrophe, and multi-valued trajectories.