Frontiers in the study of chaotic dynamical systems with open problems
Literaturangaben
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| Weitere Verfasser: | , |
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
New Jersey, London u.a.
World Scientific
2011
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| Schriftenreihe: | World scientific series on nonlinear science / B
16 |
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| Online Zugang: | Inhaltsverzeichnis Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | Literaturangaben 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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| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | VIII, 258 S. graf. Darst. |
| ISBN: | 9814340693 981-4340-69-3 9789814340694 978-981-4340-69-4 |