Nonlinear dynamics and its applications have been under intensive studies during last two decades. However, trivial random noise may lead to unpredictable consequences. Nowadays stochastic dynamics has raised interests in many fields, such as physical science, life science, chaotic electric circuits, and nonlinear psychology. This book describes the models of random dynamics which are from applications in various fields. Some illustrative models are presented to demonstrate how to model random phenomena sciences and engineering, how to quantify rare or significant events in these models, how to investigate stochastic dynamics of complex systems, and how to interpret dynamical results in real applications. Some efficient methods, both numerical and theoretical, to study stochastic systems are presented in an accessible way. This book will be an ideal starting point for those who needs a basic fundamental understanding of stochastic dynamical systems. The audience will be graduate students, engineers, junior researchers in applied mathematics, mechanics, probability and statistics and other professionals who are interested in the subject.

Dr. Wei Xu is Professor of applied mathematics at Northwestern Polytechnical University, CHINA. His expertise is in stochastic dynamics and its applications. He has made numerous contributions to stochastic dynamics.