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自治和非自治不连续微分方程中的分岔（英文版）

样章
作者：
Marat Akhmet， Ardak Kashkynbayev
定价：
69.00元
ISBN：
978-7-04-047450-3
版面字数：
180.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2017-05-09
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
暂无
  • 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

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