This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.
Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine (S OuYang & Y Lin); Nonexistence of Chaotic Solutions of Nonlinear Differential Equations (L S Yao); Dynamics of Quadratic and Higher Degree Polynomial ODE Systems (J Heidel & F Zhang); On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems (G M Mahmoud); On the Study of Chaotic Systems with Non-Horseshoe Template (A Ray et al.); Instability of Solutions of Fourth and Fifth Order Delay Differential Equations (C Tunc); Some Conjectures about the Synchronizability and the Topology of Networks (A Caneco et al.); Wavelet Study of Dynamical Systems using Partial Differential Equations (E B Postnikov); Combining the Dynamics of Discrete Dynamical Systems (J S Canovas); Code Structure for Pairs of Linear Maps with Some Open Problems (P Troshin); Recent Advances in Open Billiards with Some Open Problems (C P Dettmann); Open Problems in the Dynamics of the Expression of Gene Interaction Networks (L S Liebovitch & V Naudot); How to Transform a Type of Chaos in Dynamical Systems (E Zeraoulia & J C Sprott).