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; Poincare maps and map-dynamics; empirical computational sciences vis-a-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 areas in which these concepts appear include optics, geophysics, meteorology, hydrodynamics, plasma physics, accelerators, astrophysics, chemical dynamics, lattice dynamics, ecology, mathematical biology, electrical and mechanical systems. A number of experimental studies, which employ these theoretical concepts in these fields of research, are also discussed. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographic notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathematics, chemistry, biology, and engineering will welcome this book as the first broad introduction to this important major field of research.
