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.
- 目录
- <span id="catalog_all" style="">1 Introduction
- 1.1 Discontinuous systems
- 1.2 Book layout
- References
- 2 Flow Switchability
- 2.1 Discontinuous dynamic systems
- 2.2 G-functions
- 2.3 Passable flows
- 2.4 Non-passable flows
- 2.5 Tangential flows
- 2.6 Switching bifurcations
- References
- 3 Transversality and Sliding Phenomena
- 3.1 A controlled system
- 3.2 Transversality conditions
- 3.3 Mappings and predictions
- 3.4 Periodic and chaotic motions
- References
- 4 A Frictional Oscillator on Time-varying Belt
- 4.1 Mechanical model
- 4.2 Analytical conditions
- 4.3 Generic mappings and force product criteria...
- 4.4 Periodic motions
- 4.5 Numerical simulations
- References
- 5 Two Oscillators with Impacts and Stick
- 5.1 Physical problem
- 5.2 Domains and vector fields
- 5.3 Mechanism of stick and grazing
- 5.4 Mapping structures and motions
- 5.5 Periodic motion prediction
- 5.6 Numerical illustrations
- References
- 6 Dynamical Systems with Frictions
- 6.1 Problem statement
- 6.2 Switching and stick motions
- 6.3 Periodic motions
- 6.4 Numerical illustrations
- References
- 7 Principles for System Interactions
- 7.1 Two dynamical systems
- 7.2 Fundamental interactions
- 7.3 Interactions with singularity
- 7.4 Interactions with comer singularity
- References
- Appendix
- A.1 Basic solution
- A.2 Stability and bifurcation
- Index </span>
