Stochastic Averaging Methods and Applications, Volume 1

The stochastic averaging methods are among the most effective and widely applied approximate methods for studying nonlinear stochastic dynamics. Upon an overview of global research on the subject, the book highlights a comprehensive summary of research results obtained by the group led by Professor Weiqiu Zhu at Zhejiang University in China and the group led by Professors Y. K. Lin and G. Q. Cai at Florida Atlantic University in the USA over the past three decades. The books are structured to progress logically from foundational principles to simple problems and then to increasingly complex applications. To facilitate understanding and mastery of the methods, the books offer essential preliminary knowledge and a wealth of examples.

The book comprises two volumes. Volume 1 introduces the basic principles of stochastic averaging methods and their applications to single-degree-of-freedom systems under various random excitations. It also covers stochastic averaging methods for quasi-Hamiltonian systems subjected to different random excitations, including Gaussian white noise, combined Gaussian and Poisson white noises, and fractional Gaussian noise. Volume 2 explores stochastic averaging methods for quasi-integrable Hamiltonian systems under colored noise excitation, quasi-integrable Hamiltonian systems with genetic effects under Gaussian white noise and colored noise excitations, and quasi-generalized Hamiltonian systems under Gaussian white noise excitation. Additionally, it covers applications of these methods in ecosystems and some other natural science and engineering scenarios.

These books serve as both introductory texts and valuable reference resources for readers in higher education and research institutions who are interested in or actively engaged in research involving nonlinear stochastic dynamics. The fields covered include mechanics, physics, chemistry, biology, ecology, astronautics and aeronautics, oceanography, civil engineering, mechanical engineering, and electrical engineering.

Introduction.- Random Process.- Nonlinear Stochastic Dynamical System.- Stochastic Averaging Method for Single DOF System.

Weiqiu Zhu is a professor of mechanics in Zhejiang University, China and academician of Chinese Academy of Sciences. He worked in the field of random vibration and stochastic dynamics for over four decades and conducted long-term cooperative study with Prof. S.H. Crandall at Massachusetts Institute of Technology and Prof. Y.K. Lin at Florida Atlantic University, the USA. During past three decades, he and his research team developed the nonlinear stochastic dynamics and control in Hamiltonian formulation. He published 260 papers on international peer review journals and three monographs. He was the chairman of the fifth International Conference on Stochastic Structural Dynamics in 2003 and IUTAM Symposium on Nonlinear Stochastic Dynamics and Control in 2010, and was Editor-in-Chief of proceedings of the conferences. He was editorial board member of seven international journals. He won the second prize of China National Natural Science Awards and is one of the World’s Top 2% Scientists 2023 (career-long impact).