This book covers developments in the field of the theory of oscillations from the diverse viewpoints, reflecting the field's multidisciplinary nature. Addressing researchers and students in mechanics, physics, applied mathematics, and engineering, it describes the state of the art in this area, including applications. Because of its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and a reference for specialists. This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems.
Special attention is given to efficient numerical implementations of the developed techniques.
Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for PhD students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the 1st edition while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis. This volume is concerned with various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems, especially with the long-term behaviour of the perturbed system.