离散化与隐映射动力学（英文版）
作者： 罗朝俊
出版时间：2015-09
出版社：高等教育出版社
- 高等教育出版社
- 9787040428353
- 1版
- 70798
- 46253978-4
- 精装
- 16开
- 2015-09
- 280
- 310
- 工学
- 力学
- O322
- 物理类
- 本科 研究生及以上
《离散化与隐映射动力学（英文版）》系统介绍了连续系统的离散化方法，并提出非线性动力系统的隐映射动力学，同时用于预测非线性连续系统从周期运动到混沌的复杂性。书中首先回顾了离散非线性动力系统中不动点稳定性和分岔理论，通过单步和多步离散化较完整地建立了连续动力系统的显映射和隐映射算法，并系统地讨论了非线性离散系统的周期-M解的隐映射动力学。提出了非线性连续系统周期解到混沌解的半解析法。
本书可作为应用数学，物理，力学，控制和其他工程学科的高年级大学生、研究生、教授、以及科研人员和工程技术人员的参考书。
1 Introduction
1.1 A Brief History
1.2 Book Layout
References
2 Nonlinear Discrete Systems
2.1 Definitions
2.2 Fixed Points and Stability
2.3 Stability Switching Theory
2.4 BifurcatioTheory
References
3 Discretizatioof Continuous Systems
3.1 Continuous Systems
3.2 Basic Discretization
3.2.1 Forward Euler's Method
3.2.2 Backward Euler's Method
3.2.3 Trapezoidal Rule Discretization
3.2.4 Midpoint Method
3.3 Introductioto Runge-Kutta Methods
3.3.1 Taylor Series Method
3.3.2 Runge-Kutta Method of Order 2
3.4 Explicit Runge-Kutta Methods
3.4.1 Runge-Kutta Method of Order 3
3.4.2 Runge-Kutta Method of Order 4
3.5 Implicit Runge-Kutta Methods
3.5.1 Polynomial Interpolation
3.5.2 Implicit Runge-Kutta Methods
3.5.3 Gauss Method
3.5.4 Radau Method
3.5.5 Lobatto Method
3.5.6 Diagonally Implicit RK Methods
3.5.7 Stability of Implicit Runge-Kutta Methods.
3.6 Multi-step Methods
3.6.1 Adams-Bashforth Methods
3.6.2 Adams-MoultoMethods
3.6.3 Explicit Adams Methods
3.6.4 Implicit Adams Methods
3.6.5 General Forms
3.7 Generalized Implicit Multi-step Methods
References
4 Implicit Mapping Dynamics
4.1 Single-Step Implicit Maps
4.2 Discrete Systems with Multiple Maps
4.3 Complete Dynamics of a HenoMap System
4.4 Multi-step Implicit Maps
References
5 Periodic Flows iContinuous Systems
5.1 Continuous Nonlinear Systems
5.2 Continuous Time-Delay Systems
5.2.1 Interpolated Time-Delay Nodes
5.2.2 Integrated Time-Delay Nodes
5.3 Discrete Fourier Series
References
6 Periodic Motions to Chaos iDuffing Oscillator
6.1 Period- 1 Motions
6.2 Period-m Motions
6.3 BifurcatioTrees of Periodic Motions
6.4 Frequency-Amplitude Characteristics
6.4.1 Period-1 Motions to Chaos
6.4.2 Period-3 Motions
6.5 Numerical Simulations
Reference
Index
