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内容大纲
本书内容涉及离散和连续时间动力系统的70个不同主题，共9章，介绍了研究混沌动力系统的一些方法，阐述了将人类免疫缺陷病毒和城市化动态作为离散映射不太受欢迎的主题的示例，收集了用严格证明二维分段映射中混沌的不同方法的结果，对神经网络模型中的鲁棒混沌具有的许多说明性示例和方法进行了讨论，给出了某些已经严格确定的二维离散映射的李雅普诺夫指数的一些结果，讨论了利用深入的相关方法来证明某些形式的离散时间系统和连续时间系统的有界性，展示了全局渐近稳定离散时间映射和连续时间系统的若干形式的某些定义及相关结果等。 -
作者介绍
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目录
Preface
1. Review of Chaotic Dynamics
1.1 Introduction
1.2 Poincare map technique
1.3 Smale horseshoe
1.4 Symbolic dynamics
1.5 Strange attractors
1.6 Basins of attraction
1.7 Density, robustness and persistence of chaos
1.8 Entropies of chaotic attractors
1.9 Period 3 implies chaos
1.10 The Snap-back repeller and the Li-Chen-Marotto theorem
1.11 Shilnikov criterion for the existence of chaos
2. Human lmmunodeficiency Virus and Urbanization Dynamics
2.1 Introduction
2.2 Definition of Human lmmunodeficiency Virus (HIV)
2.3 Modelling the Human Immunodeficiency Virus (HIV)
2.4 Dynamics of sexual transmission of the Human Immunodeficiency Virus
2.5 The effects of variable infectivity on the HIV dynamics
2.6 The CD4+ Lymphocyte dynamics in HIV infection
2.7 The viral dynamics of a highly pathogenic Simian/Human Immunodeficiency Virus
2.8 The effects of morphine on Simian lmmunodeficiency Virus Dynamics
2.9 The dynamics of the HIV therapy system
2.10 Dynamics of urbanization
3. Chaotic Behaviors in Piecewise Linear Mappings
3.1 Introduction
3.2 Chaos in one-dimensional piecewise smooth maps
3.3 Chaos in one-dimensional singular maps
3.4 Chaos in 2-D piecewise smooth maps
4. Robust Chaos in Neural Networks Models
4.1 Introduction
4.2 Chaos in neural networks models
4.3 Robust chaos in discrete time neural networks
4.3.1 Robust chaos in I-D piecewise-smooth neural networks
4.3.2 Fragile chaos (blocks with smooth activation function)
4.3.3 Robust chaos (blocks with non-smooth activation function)
4.3.4 Robust chaos in the electroencephalogram model
4.3.5 Robust chaos in Diluted circulant networks
4.3.6 Robust chaos in non-smooth neural networks
4.4 The importance of robust chaos in mathematics and some open problems
5. Estimating Lyapunov Exponents of 2-D Discrete Mappings
5.1 Introduction
5.2 Lyapunov exponents of the discrete hyperchaotic double scroll map
5.3 Lyapunov exponents for a class of 2-D piecewise linear mappings
5.4 Lyapunov exponents of a family of 2-D discrete mappings with separate variables
5.5 Lyapunov exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law
5.6 Lyapunov exponents of a modified map-based BVP model
6. Control, Synchronization and Chaotification of Dynamical Systems
6.1 Introduction
6.2 Compound synchronization of different chaotic systems
6.3 Synchronization of 3-D continuous-time quadratic systems using a universal non-linear control law
6.4 Co-existence of certain types of synchronization and its inverse
6.5 Synchronization of 4-D continuous-time quadratic systems using a universal non-linear control law
6.6 Quasi-synchronization of systems with different dimensions
6.7 Chaotification of 3-D linear continuous-time systems using the signum function feedback
6.8 Chaos control problem of a 3-D cancer model with structured uncertainties
6.9 Controlling homoclinic chaotic attractor
6.10 Robustification of 2-D piecewise smooth mappings
6.11 Chaotifying stable n-D linear maps via the controller of any bounded function
7. Boundedness of Some Forms of Quadratic Systems
7.1 Introduction
7.2 Boundedness of certain forms of 3-D quadratic continuous-time systems
7.3 Bounded jerky dynamics
7.3.1 Boundedness of general forms of jerky dynamics
7.3.2 Examples of bounded jerky chaos
7.3.3 Appendix A
7.4 Bounded hyperjerky dynamics
7.5 Boundedness of the generalized 4-D hyperchaotic model containing Lorenz-Stenflo and Lorenz-Haken systems
7.5.1 Estimating the bounds for the Lorenz-Haken system
7.5.2 Estimating the bounds for the Lorenz-Stenflo system
7.6 Boundedness of2-D H~non-like mapping
7.7 Examples of fully bounded chaotic attractors
8. Some Forms of Globally Asymptotically Stable Attractors
8.1 Introduction
8.2 Direct Lyapunov stability for ordinary differential equations
8.3 Exponential stability of non-linear time-varying
8.4 Lasalle's Invariance Principle
8.5 Direct Lyapunov-type stability for fractional-like systems
8.6 Construction of globally asymptotically stable n-D discrete mappings
8.7 Construction ofsuperstable n-D mappings
8.8 Examples of globally superstable l-D quadratic mappings
8.9 Construction of globally superstable 3-D quadratic mappings
8.10 Hyperbolicity of dynamical systems
8.11 Consequences of uniform hyperbolicity
8.11.1 Classification of singular-hyperbolic attracting sets
8.12 Structural stability for 3-D quadratic mappings
8.12.1 The concept of structural stability
8.12.2 Conditions for structural stability
8.12.3 The Jordan normal form J
8.12.4 The Jordan normal form dE
8.12.5 The Jordan normal form J
8.12.6 The Jordan normal formJ
8.12.7 The Jordan normal formJ
8.12.8 The Jordan normal form J
8.13 Construction of globally asymptotically stable partial differential systems
8.14 Construction of globally stable system of delayed differential equations
8.15 Stabilization by the Jurdjevic-Quinn method
8.15.1 The minimization problem
8.15.2 The inverse optimi
9. Transformation of Dynamical Systems to Hyperjerky Motions
9.1 Introduction
9.2 Transformation of 3-D dynamical systems to jerk form
9.3 Transformation of 3-D dynamical systems to rational and cubic jerks forms
9.4 Transformation of 4-D dynamical systems to hyperjerk form
9.4.1 The expression of the transformation between (9.45) and (9.61)-(9.62)
9.4.2 Examples of4-D hyperjerky dynamics
9.5 Examples of crackle and top dynamics
References
Index
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