Stochastic Averaging

This book highlights a comprehensive summary of the basics of Stochastic averaging method in various systems and its applications in science and engineering. The Stochastic averaging method is the most powerful and most widely applied approximate analytical method for studying nonlinear stochastic dynamics, including response prediction, stability determination and reliability estimation. This book presents the basic principle of the method, the stochastic averaging method for several kinds of dynamical systems (one-DOF systems, quasi Hamiltonian systems, quasi generalized Hamiltonian systems, quasi Hamiltonian systems with genetic effector, etc.) and several kinds of random excitations (Gaussian white noise, Gaussian and Poisson white noises, fractional Gaussian noise, coloured noise, combination of harmonic function and wideband noise, etc.), and the applications of the method in sciences and engineering. A significant part of the book covers research results by Prof. Weiqiu Zhu and his research term in China and by Profs. Y.K. Lin and G.Q. Cai in the USA during the past three decades. The book explains the profound theory in simple terms and provides the necessary preparatory knowledge and abundant examples to help readers easily understand and put the method in use. The target audiences include the scientists, engineers, teachers and graduate students of a number of disciplines of sciences (physics, chemistry, biology, ecology, etc.) and engineering (mechanical, civil, ocean, electrical power engineering, etc.).