离散化与隐映射动力学（英文版）

Discretization and implicit mapping dynamics are crucial methods in the study of continuous nonlinear systems. In this book, author Prof. Luocha jun first reviews the stability of fixed points and the bifurcation theory in nonlinear discrete systems, and then presents a comprehensive introduction to the explicit and implicit discretization of continuous systems, including Runge-Kutta methods, multi-step methods, and implicit multi-step methods. The book also discusses the implicit mapping dynamics of nonlinear discrete systems, including the mapping algorithm of single-step and multi-step mappings, and the hidden mapping dynamics of periodic-M solutions in nonlinear discrete systems. Moreover, the author proposes a semi-analytical method for predicting the period solution to chaos solution in nonlinear continuous systems. Notably, the book introduces the effective processing method of time-delay points in discrete-time-delay continuous systems, as well as the discrete Fourier series of nonlinear continuous systems with periodic motion. Through numerical simulations and analyses of the Duffing oscillator, the book presents the bifurcation trees of periodic motions and their corresponding frequency-amplitude characteristics, including period-1 and period-m motions to chaos.In summary, Discretization and Implicit Mapping Dynamics: A Systematic Approach to Continuum Mechanics provides a comprehensive and detailed introduction to the methods and theories of discretization and implicit mapping dynamics for continuous nonlinear systems. It is recommended for researchers, students and academics in applied sciences and engineering fields interested in the dynamics and control of nonlinear systems.