Ebook: Frontiers in the study of chaotic dynamical systems with open problems

Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments.This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks and anomalous diffusion.A first-class board of international scientists advises the editor, such that the carefully selected and invited contributions represent the latest and most relevant findings 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