Nonlinear Dynamics of Time Delay Systems: Methods and Applications

This book presents research advancements in the dynamics of systems with time delay conducted by the group led by Professor Jian Xu. Addressing the challenges arising from the joint impact of time delay and nonlinearity, novel theoretical approaches are developed to formulate the nonlinear response of the system. This facilitates the classification of complex nonlinear dynamics, especially the non-resonant and resonant double Hopf bifurcation. In contrast to systems without time delay, time delay systems require specific considerations when identifying system parameters, particularly the time delay. Consequently, inverse problems of systems with time delay are also explored in this book. Moreover, detailed investigations on vibration suppression methods and experimental prototypes based on time delay, such as time delay isolators with quasi-zero stiffness, are conducted. Simultaneously, this book is enriched with a large number of case studies ranging from manufacturing, network science, biology, and public transportation, illuminating the mechanisms of delay-induced nonlinear dynamics in practical applications. This book is suitable for graduate students and researchers who are eager to understand the delay-induced nonlinear dynamics, or technical personnel in whose projects small variations of time delay may cause significant changes in system responses. 

Jian Xu received his Ph.D. degree in Dynamics and Control at Tianjin University, Tianjin, China, in 1994. Currently, he holds the position of Distinguished Professor and serves as the Director of the Institute on Dynamics and Control at Tongji University, Shanghai, China. He served as a Postdoctoral Researcher at Beihang University, Beijing, China, from 1994 to 1996, and later at Huazhong University of Science and Technology, Wuhan, China, from 1996 to 1998. In 1998, he joined Tongji University as an associate professor and has held the position of professor since 2000. His primary research interests includes time delay-induced dynamics, locomotion robotics, nonlinear dynamics and control in natural and engineering systems, and vibration control. He has authored over 200 peer-reviewed journal papers, two academic books, and a textbook. He received the National Science Fund for Outstanding Young Scholars (2006), and was awarded the Leading Talent of Shanghai (2008), the Shanghai Outstanding Academic Leader (2007), and the Model Teacher of Shanghai (2009).