3 Kicked Mechanical Models and Differential Equations with Periodic Switch

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Hyperbolic Chaos: A Physicist`s View双曲混作者：Sergey P. Kuznetsov　　 ISBN：978-7-04-031964-4　出版时间：2011-09-14

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目录

Front Matter

Part I Basic Notions and Review

1 Dynamical Systems and Hyperbolicity

2 Possible Occurrence of Hyperbolic Attractors

Part II Low-Dimensional Models

3 Kicked Mechanical Models and Differential Equations with Periodic Switch

4 Non-Autonomous Systems of Coupled Self-Oscillators

5 Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincar´e Maps

6 Parametric Generators of Hyperbolic Chaos

7 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches

Part III Higher-Dimensional Systems and Phenomena

8 Systems of Four Alternately Excited Non-autonomous Oscillators

9 Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle

10 Systems with Time-delay Feedback

11 Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators

Part IV Experimental Studies

12 Electronic Device with Attractor of Smale-Williams Type

13 Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps

14 Conclusion

Appendix A Computation of Lyapunov Exponents:The Benettin Algorithm

Appendix B H´enon and Ikeda Maps

Appendix C Smale’s Horseshoe and Homoclinic Tangle

Appendix D Fractal Dimensions and Kaplan-Yorke Formula

Appendix E Hunt’s Model: Formal Definition

Appendix F Geodesics on a Compact Surface of Negative Curvature

AppendixG Effect of Noise in a System with a Hyperbolic Attractor

Index
- 3.1 Smale-Williams solenoid in mechanical model: Motion of a particle on a plane under periodic kicks
- 3.2 A set of switching differential equations with attractor of Smale-Williams type
- 3.3 Explicit dynamical system with attractor of Plykin type
- 3.3.1 Plykin type attractor on a sphere
- 3.3.2 Plykin type attractor on the plane
- 3.4 Plykin-like attractor in smooth non-autonomous system
- References

3 Kicked Mechanical Models and Differential Equations with Periodic Switch

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