简介
《离散化与隐映射动力学（英文版）（精）》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。 罗朝俊教授为非线性动力学和力学领域的国际知名学者。美国南伊利诺伊大学的杰出教授，主要研究领域为哈密顿系统混沌、非线性变形体动力学、不连续动力系统、非线性系统的规则性和复杂性和微分方程的解析解与数值解。 首次展示了非线性连续系统周期解到混沌解的隐映射动力学讨论连续系统的显映射和隐映射算法建立了非线性离散动力系统中周期-M解的隐映射动力学提出了时滞和非时滞非线性连续系统中周期解和混沌解的半解析法展现时滞连续系统离散过程中时滞点的有效处理方法系统讨论了非线性连续系统周期运动的离散傅里叶级数
目录
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 Bifurcation Theory
References
3 Discretization of 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 Introduction to 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-Moulton Methods
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 Henon Map System
4.4 Multi-step Implicit Maps
5 References.
Periodic Flows in Continuous 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
6 References
6 Periodic Motions to Chaos in Duffing Oscillator
6.1 Period- 1 Motions
6.2 Period-m Motions
6.3 Bifurcation Trees 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
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 Bifurcation Theory
References
3 Discretization of 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 Introduction to 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-Moulton Methods
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 Henon Map System
4.4 Multi-step Implicit Maps
5 References.
Periodic Flows in Continuous 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
6 References
6 Periodic Motions to Chaos in Duffing Oscillator
6.1 Period- 1 Motions
6.2 Period-m Motions
6.3 Bifurcation Trees 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
Discretization and Implicit Mapping Dyna
- 名称
- 类型
- 大小
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