自治和非自治不连续微分方程中的分岔(英文版)(精)/非线性物理科学

阿克梅特、卡什金巴耶夫著的这本《自治和非自 治不连续微分方程中的分岔（英文版）》主要讨论不 同类型的自治和非自治不连续微分方程中的分岔。那 些具有跳跃的微分方程既可以是右端点不连续的，也 可以是在轨迹上不连续，或是方程解的区间常数近似 的。本书的结果可以应用于各个领域，如神经网络、 脑动力学、机械系统、天气现象、人口动力学等。毫 无疑问，分岔理论应该进一步发展到不同类型的微分 方程。在这个意义上，本书将是这个领域的首创。读 者将从本书了解到该理论的新成果，学会如何将该理 论应用到不同类型的不连续微分方程的具体方法。此 外，读者将学习到分析这些方程的非自治分岔情况的 新方法。 本书无论是对初学者还是对该领域的专家都非常 有帮助。对于初学者它提供了一个很深的印象，即分 岔理论不仅可以应用于离散和连续系统，也可应用于 以各种不同方式组合的这些系统。对于该领域的专家 ，他们将在本书中发现一些强大的工具，这些工具可 应用于冲击瞬间可变的不连续动力系统、有解分段常 数化的一般类型的微分方程以及Filippov系统。本书 对研究带脉冲系统中的分岔的学者也是非常有益的， 因为这些分岔往往是非自治系统的。

1 Introduction 1.1 General Descriptioof 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 Bemoulli Equations 1.4 Organizatioof the Book 2 Hopf BifurcatioiImpulsive Systems 2.1 Hopf Bifurcatioof 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 Bifurcatioof 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 Bifurcatioof Periodic Solutions 2.2.6 Examples 2.3 Periodic Solutions of the Vader Pol Equation 2.3.1 Introductioand Preliminaries 2.3.2 Theoretical Results 2.3.3 Center Manifold 2.4 Notes 3 Hopf BifurcatioiFilippov 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 Bifurcatioof Periodic Solutions 3.1.6 AExample 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 Bifurcatioof Periodic Solutions 3.2.6 AExample 3.3 Notes 4 Nonautonomous BifurcatioiImpulsive 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 Introductioand Preliminaries 4.2.2 Bounded Solutions 4.2.3 The Pitchfork Bifufcation 4.2.4 The Transcritical Bifurcation 4.2.5 Illustrative Examples 4.3 Notes 5 Nonautonomous Bifurcations iNonsolvable Impulsive Systems 5.1 The Transcritical and the Pitchfork Bifurcations 5.1.1 Introduction 5.1.2 Preliminaries 5.1.3 Attractivity and Repulsivity ia 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 Introductioand Preliminaries 5.2.2 Attractivity and Repulsivity ia Linear Nonhomogeneous Impulsive System 5.2.3 BifurcatioAnalysis 5.2.4 AExample 5.3 Notes 6 Nonautonomous Bifurcations iBernoulli Differential Equations with Piecewise Constant Argument of Generalized Type 6.1 Introductioand Preliminaries 6.1.1 Attractioand Stability 6.2 Bounded Solutions 6.3 The Pitchfork Bifurcation 6.4 The Transcritical Bifurcation 6.5 Illustrative Examples 6.6 Notes References