Frontiers in the study of chaotic dynamical systems with open problems 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 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 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 Parrondos Paradox and Commuting Functions 9.3.2 Dynamics Shared by Commuting Functions Machine generated contents note 1 Problems with Lorenzs Modeling and the Algorithm of Chaos Doctrine Y. Lin 1.1 Introduction 1.2 Lorenzs Modeling and Problems of the Model 1.3 Computational Schemes and What Lorenzs 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