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Frontiers in the Study of Chaotic Dynamical Systems With Open Problems [electronic resource]

edited by Elhadj Zeraoulia, Julien Clinton Sprott
Format
EBook; Book; Online
Published
Singapore ; Hackensack, N.J. : World Scientific, c2011.
Language
English
Series
World Scientific Series on Nonlinear Science. Series B. Special Theme Issues and Proceedings
World Scientific Series on Nonlinear Science Series B Special Theme Issues and Proceedings
ISBN
9789814340694, 9814340693
Contents
  • 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
  • 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
  • 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
  • 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
  • 6. Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / C. Tunc
  • 6.1. Introduction
  • 6.2. Open Problems
  • 6.3. Conclusion
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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.
Description
Mode of access: World wide Web.
Notes
Includes bibliographical references and indexes.
Series Statement
World Scientific series on nonlinear science. Series B. Special theme issues and proceedings ; v. 16
World Scientific series on nonlinear science. Series B, Special theme issues and proceedings ; v. 16
Copyright Not EvaluatedCopyright Not Evaluated
Technical Details
  • Access in Virgo Classic
  • Staff View

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    a| Frontiers in the study of chaotic dynamical systems with open problems h| [electronic resource] / c| edited by Elhadj Zeraoulia, Julien Clinton Sprott.
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    g| Machine generated contents note: g| 1. t| Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / r| Y. Lin -- g| 1.1. t| Introduction -- g| 1.2. t| Lorenz's Modeling and Problems of the Model -- g| 1.3. t| Computational Schemes and What Lorenz's Chaos Is -- g| 1.4. t| Discussion -- g| 1.5. t| Appendix: Another Way to Show that Chaos Theory Suffers From Flaws -- t| References -- g| 2. t| Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / r| L. S. Yao -- g| 2.1. t| Introduction -- g| 2.2. t| Open Problems About Nonexistence of Chaotic Solutions -- t| References -- g| 3. t| Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / r| J. Heidel -- g| 3.1. t| First Open Problem -- g| 3.2. t| Second Open Problem -- g| 3.3. t| Third Open Problem -- g| 3.4. t| Fourth Open Problem -- g| 3.5. t| Fifth Open Problem -- g| 3.6. t| Sixth Open Problem -- t| References -- g| 4. t| On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / r| G. M. Mahmoud
    505
    0
    0
    g| 4.1. t| Introduction -- g| 4.2. t| Examples -- g| 4.2.1. t| Dynamical Properties of Chaotic Complex Chen System -- g| 4.2.2. t| Hyperchaotic Complex Lorenz Systems -- g| 4.3. t| Open Problems -- g| 4.4. t| Conclusions -- t| References -- g| 5. t| On the Study of Chaotic Systems with Non-Horseshoe Template / r| S. Basak -- g| 5.1. t| Introduction -- g| 5.2. t| Formulation -- g| 5.3. t| Topological Analysis and Its Invariants -- g| 5.4. t| Application to Circuit Data -- g| 5.4.1. t| Search for Close Return -- g| 5.4.2. t| Topological Constant -- g| 5.4.3. t| Template Identification -- g| 5.4.4. t| Template Verification -- g| 5.5. t| Conclusion and Discussion -- t| References -- g| 6. t| Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / r| C. Tunc -- g| 6.1. t| Introduction -- g| 6.2. t| Open Problems -- g| 6.3. t| Conclusion -- t| References -- g| 7. t| Some Conjectures About the Synchronizability and the Topology of Networks / r| S. Fernandes -- g| 7.1. t| Introduction -- g| 7.2. t| Related and Historical Problems About Network Synchronizability -- g| 7.3. t| Some Physical Examples About the Real Applications of Network Synchronizability
    505
    0
    0
    g| 7.4. t| Preliminaries -- g| 7.5. t| Complete Clustered Networks -- g| 7.5.1. t| Clustering Point on Complete Clustered Networks -- g| 7.5.2. t| Classification of the Clustering and the Amplitude of the Synchronization Interval -- g| 7.5.3. t| Discussion -- g| 7.6. t| Symbolic Dynamics and Networks Synchronization -- t| References -- g| 8. t| Wavelet Study of Dynamical Systems Using Partial Differential Equations / r| E. B. Postnikov -- g| 8.1. t| Definitions and State of Art -- g| 8.2. t| Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori -- g| 8.3. t| The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case -- g| 8.4. t| Discussion of Open Problems -- t| References -- g| 9. t| Combining the Dynamics of Discrete Dynamical Systems / r| J. S. Canovas -- g| 9.1. t| Introduction -- g| 9.2. t| Basic Definitions and Notations -- g| 9.3. t| Statement of the Problems -- g| 9.3.1. t| Dynamic Parrondo's Paradox and Commuting Functions -- g| 9.3.2. t| Dynamics Shared by Commuting Functions
    505
    0
    0
    g| 9.3.3. t| Computing Problems for Large Periods T -- g| 9.3.4. t| Commutativity Problems -- g| 9.3.5. t| Generalization to Continuous Triangular Maps on the Square -- t| References -- g| 10. t| Code Structure for Pairs of Linear Maps with Some Open Problems / r| P. Troshin -- g| 10.1. t| Introduction -- g| 10.2. t| Iterated Function System -- g| 10.3. t| Attractor of Pair of Linear Maps -- g| 10.4. t| Code Structure of Pair of Linear Maps -- g| 10.5. t| Sufficient Conditions for Computing the Code Structure -- g| 10.6. t| Conclusion and Open Questions -- t| References -- g| 11. t| Recent Advances in Open Billiards with Some Open Problems / r| C. P. Dettmann -- g| 11.1. t| Introduction -- g| 11.2. t| Closed Dynamical Systems -- g| 11.3. t| Open Dynamical Systems -- g| 11.4. t| Open Billiards -- g| 11.5. t| Physical Applications -- g| 11.6. t| Discussion -- t| References -- g| 12. t| Open Problems in the Dynamics of the Expression of Gene Interaction Networks / r| V. Naudot -- g| 12.1. t| Introduction -- g| 12.2. t| Attractors for Flows and Diffeomorphisms
    505
    0
    0
    g| 12.3. t| Statement of the Problem -- g| 12.3.1. t| A First Attempt -- g| 12.3.2. t| Examples -- g| 12.4. t| Experimental Information -- g| 12.5. t| Theoretical Models of Gene Interaction -- g| 12.6. t| Conclusions -- t| References -- g| 13. t| How to Transform a Type of Chaos in Dynamical Systems? / r| J. C. Sprott -- g| 13.1. t| Introduction -- g| 13.2. t| Hyperbolification of Dynamical Systems -- g| 13.3. t| Transforming Dynamical Systems to Lorenz-Type Chaos -- g| 13.4. t| Transforming Dynamical Systems to Quasi-Attractor Systems -- g| 13.5. t| A Common Classification of Strange Attractors of Dynamical Systems -- t| References.
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