Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics.

This book mainly focuses on the switchability of discontinuous dy-namical systems on time-varying domains. Based on such concepts, prin-ciples of dynamical system interactions without any connections are pre-sented. This book consists of seven chapters. Chapter 1 discusses two examples to show where discontinuous dynamical systems exist. Chapter 2 presents a basic theory for the switchability of a flow to the separation boundary in discontinuous dynamical systems, and switching bifurca-tions are also addressed. In Chapter 3, transversality and sliding phenomena for a controlled dynamical system to an inclined line boundary of control logic are presented to show how to apply such a new theory. In Chapter 4, dynamics of a frictional oscillator on a traveling belt with time-varying speeds is presented, which is a simple example of discon-tinuous dynamical systems on the time-varying domains. Chapter 5 pre-sents the dynamics mechanism of impacting chatter and stick phenomena in two dynamical systems with impact laws. In Chapter 6, dynamical behaviors of two systems connected with friction are presented. In Chapters 3 6, the similar writing styles and formats are adopted to show how to apply the new theory to different problems. In Chapter 7, a generalized theory for the interaction principle of dynamical systems is developed from discontinuous dynamical systems on time-varying domains.