Frontiers in the study of chaotic dynamical systems with open problems [electronic resource] / edited by Elhadj Zeraoulia, Julien Clinton Sprott.

Includes bibliographical references and indexes.

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.

Description based on print version record.