Frontiers in the study of chaotic dynamical systems with open problems /

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Zeraoulia, Elhadj (Editor ), Sprott, Julien C. (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific, ©2011.
Colección:World Scientific series on nonlinear science. Special theme issues and proceedings ; v. 16.
Temas:
Chaotic behavior in systems.
Dynamics.
Chaos.
Dynamique.
SCIENCE > Chaotic Behavior in Systems.
Chaotic behavior in systems
Dynamics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: 1. Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / Y. Lin
  • 1.1. Introduction
  • 1.2. Lorenz's Modeling and Problems of the Model
  • 1.3. Computational Schemes and What Lorenz's Chaos Is
  • 1.4. Discussion
  • 1.5. Appendix: Another Way to Show that Chaos Theory Suffers From Flaws
  • References
  • 2. Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / L.S. Yao
  • 2.1. Introduction
  • 2.2. Open Problems About Nonexistence of Chaotic Solutions
  • References
  • 3. Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / J. Heidel
  • 3.1. First Open Problem
  • 3.2. Second Open Problem
  • 3.3. Third Open Problem
  • 3.4. Fourth Open Problem
  • 3.5. Fifth Open Problem
  • 3.6. Sixth Open Problem
  • References
  • 4. On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / G.M. Mahmoud.
  • 4.1. Introduction
  • 4.2. Examples
  • 4.2.1. Dynamical Properties of Chaotic Complex Chen System
  • 4.2.2. Hyperchaotic Complex Lorenz Systems
  • 4.3. Open Problems
  • 4.4. Conclusions
  • References
  • 5. On the Study of Chaotic Systems with Non-Horseshoe Template / S. Basak
  • 5.1. Introduction
  • 5.2. Formulation
  • 5.3. Topological Analysis and Its Invariants
  • 5.4. Application to Circuit Data
  • 5.4.1. Search for Close Return
  • 5.4.2. Topological Constant
  • 5.4.3. Template Identification
  • 5.4.4. Template Verification
  • 5.5. Conclusion and Discussion
  • References
  • 6. Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / C. Tunc
  • 6.1. Introduction
  • 6.2. Open Problems
  • 6.3. Conclusion
  • References
  • 7. Some Conjectures About the Synchronizability and the Topology of Networks / S. Fernandes
  • 7.1. Introduction
  • 7.2. Related and Historical Problems About Network Synchronizability
  • 7.3. Some Physical Examples About the Real Applications of Network Synchronizability.
  • 7.4. Preliminaries
  • 7.5. Complete Clustered Networks
  • 7.5.1. Clustering Point on Complete Clustered Networks
  • 7.5.2. Classification of the Clustering and the Amplitude of the Synchronization Interval
  • 7.5.3. Discussion
  • 7.6. Symbolic Dynamics and Networks Synchronization
  • References
  • 8. Wavelet Study of Dynamical Systems Using Partial Differential Equations / E.B. Postnikov
  • 8.1. Definitions and State of Art
  • 8.2. Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori
  • 8.3. The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case
  • 8.4. Discussion of Open Problems
  • References
  • 9. Combining the Dynamics of Discrete Dynamical Systems / J.S. Canovas
  • 9.1. Introduction
  • 9.2. Basic Definitions and Notations
  • 9.3. Statement of the Problems
  • 9.3.1. Dynamic Parrondo's Paradox and Commuting Functions
  • 9.3.2. Dynamics Shared by Commuting Functions.
  • 9.3.3. Computing Problems for Large Periods T
  • 9.3.4. Commutativity Problems
  • 9.3.5. Generalization to Continuous Triangular Maps on the Square
  • References
  • 10. Code Structure for Pairs of Linear Maps with Some Open Problems / P. Troshin
  • 10.1. Introduction
  • 10.2. Iterated Function System
  • 10.3. Attractor of Pair of Linear Maps
  • 10.4. Code Structure of Pair of Linear Maps
  • 10.5. Sufficient Conditions for Computing the Code Structure
  • 10.6. Conclusion and Open Questions
  • References
  • 11. Recent Advances in Open Billiards with Some Open Problems / C.P. Dettmann
  • 11.1. Introduction
  • 11.2. Closed Dynamical Systems
  • 11.3. Open Dynamical Systems
  • 11.4. Open Billiards
  • 11.5. Physical Applications
  • 11.6. Discussion
  • References
  • 12. Open Problems in the Dynamics of the Expression of Gene Interaction Networks / V. Naudot
  • 12.1. Introduction
  • 12.2. Attractors for Flows and Diffeomorphisms.
  • 12.3. Statement of the Problem
  • 12.3.1. A First Attempt
  • 12.3.2. Examples
  • 12.4. Experimental Information
  • 12.5. Theoretical Models of Gene Interaction
  • 12.6. Conclusions
  • References
  • 13. How to Transform a Type of Chaos in Dynamical Systems? / J.C. Sprott
  • 13.1. Introduction
  • 13.2. Hyperbolification of Dynamical Systems
  • 13.3. Transforming Dynamical Systems to Lorenz-Type Chaos
  • 13.4. Transforming Dynamical Systems to Quasi-Attractor Systems
  • 13.5. A Common Classification of Strange Attractors of Dynamical Systems
  • References.

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