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自治和非自治不连续微分方程中的分岔（英文版）

暂无简介

购买：

作者：

Marat Akhmet， Ardak Kashkynbayev

定价：

69.00元

出版时间：

2017-05-09

ISBN：

978-7-04-047450-3

物料号：

47450-00

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

动力系统

重点项目：

暂无

版面字数：

180.000千字

开本：

16开

全书页数：

暂无

装帧形式：

精装

Front Matter
1 Introduction
- 1.1 General Description of Differential Equations with Discontinuities
  - 1.1.1 Impulsive Differential Equations
  - 1.1.2 Differential Equations with Piecewise Constant Argument
  - 1.1.3 Differential Equations with Discontinuous Right-Hand Sides
- 1.2 Nonautonomous Bifurcation
- 1.3 The Bernoulli Equations
- 1.4 Organization of the Book
2 Hopf Bifurcation in Impulsive Systems
- 2.1 Hopf Bifurcation of a Discontinuous Limit Cycle
  - 2.1.1 The Nonperturbed System
  - 2.1.2 The Perturbed System
  - 2.1.3 Foci of the D-System
  - 2.1.4 The Center and Focus Problem
  - 2.1.5 Bifurcation of a Discontinuous Limit Cycle
  - 2.1.6 Examples
- 2.2 3D Discontinuous Cycles
  - 2.2.1 Introduction
  - 2.2.2 The Nonperturbed System
  - 2.2.3 The Perturbed System
  - 2.2.4 Center Manifold
  - 2.2.5 Bifurcation of Periodic Solutions
  - 2.2.6 Examples
- 2.3 Periodic Solutions of the Van der Pol Equation
  - 2.3.1 Introduction and Preliminaries
  - 2.3.2 Theoretical Results
  - 2.3.3 Center Manifold
- 2.4 Notes
3 Hopf Bifurcation in Filippov Systems
- 3.1 Nonsmooth Planar Limit Cycle from a Vertex
  - 3.1.1 Introduction
  - 3.1.2 The Nonperturbed System
  - 3.1.3 The Perturbed System
  - 3.1.4 The Focus-Center Problem
  - 3.1.5 Bifurcation of Periodic Solutions
  - 3.1.6 An Example
- 3.2 3D Filippov System
  - 3.2.1 Introduction
  - 3.2.2 The Nonperturbed System
  - 3.2.3 The Perturbed System
  - 3.2.4 Center Manifold
  - 3.2.5 Bifurcation of Periodic Solutions
  - 3.2.6 An Example
- 3.3 Notes
4 Nonautonomous Bifurcation in Impulsive Bernoulli Equations
- 4.1 The Transcritical and the Pitchfork Bifurcations
  - 4.1.1 Introduction
  - 4.1.2 Preliminaries
  - 4.1.3 The Pitchfork Bifurcation
  - 4.1.4 The Transcritical Bifurcation
- 4.2 Impulsive Bernoulli Equations: The Transcritical and the Pitchfork Bifurcations
  - 4.2.1 Introduction and Preliminaries
  - 4.2.2 Bounded Solutions
  - 4.2.3 The Pitchfork Bifurcation
  - 4.2.4 The Transcritical Bifurcation
  - 4.2.5 Illustrative Examples
- 4.3 Notes
5 Nonautonomous Bifurcations in Nonsolvable Impulsive Systems
- 5.1 The Transcritical and the Pitchfork Bifurcations
  - 5.1.1 Introduction
  - 5.1.2 Preliminaries
  - 5.1.3 Attractivity and Repulsivity in a Linear Impulsive Nonhomogeneous Systems
  - 5.1.4 The Transcritical Bifurcation
  - 5.1.5 The Pitchfork Bifurcation
- 5.2 Finite-Time Nonautonomous Bifurcations
  - 5.2.1 Introduction and Preliminaries
  - 5.2.2 Attractivity and Repulsivity in a Linear Nonhomogeneous Impulsive System
  - 5.2.3 Bifurcation Analysis
  - 5.2.4 An Example
- 5.3 Notes
6 Nonautonomous Bifurcations in Bernoulli Differential Equations with Piecewise Constant Argument of Generalized Type
- 6.1 Introduction and Preliminaries
  - 6.1.1 Attraction and Stability
- 6.2 Bounded Solutions
- 6.3 The Pitchfork Bifurcation
- 6.4 The Transcritical Bifurcation
- 6.5 Illustrative Examples
- 6.6 Notes
References