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E-grāmata: Frontiers in the Study of Chaotic Dynamical Systems with Open Problems [World Scientific e-book]

Edited by (Univ Of Wisconsin-madison, Usa), Edited by (Univ Of Tebessa, Algeria)
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Frontiers in the Study of Chaotic Dynamical Systems with Open ProblemsPalielināt
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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.
Preface v
1 Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine
1(30)
S. Ou Yang
Y. Lin
1.1 Introduction
2(2)
1.2 Lorenz's Modeling and Problems of the Model
4(7)
1.3 Computational Schemes and What Lorenz's Chaos Is
11(12)
1.4 Discussion
23(3)
1.5 Appendix: Another Way to Show that Chaos Theory Suffers From Flaws
26(3)
References
29(2)
2 Nonexistence of Chaotic Solutions of Nonlinear Differential Equations
31(12)
L. S. Yao
2.1 Introduction
31(1)
2.2 Open Problems About Nonexistence of Chaotic Solutions
32(8)
References
40(3)
3 Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems
43(16)
F. Zhang
J. Heidel
3.1 First Open Problem
44(3)
3.2 Second Open Problem
47(1)
3.3 Third Open Problem
48(2)
3.4 Fourth Open Problem
50(1)
3.5 Fifth Open Problem
51(1)
3.6 Sixth Open Problem
51(5)
References
56(3)
4 On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems
59(26)
G. M. Mahmoud
4.1 Introduction
60(6)
4.2 Examples
66(12)
4.2.1 Dynamical Properties of Chaotic Complex Chen System
66(5)
4.2.2 Hyperchaotic Complex Lorenz Systems
71(7)
4.3 Open Problems
78(1)
4.4 Conclusions
79(1)
References
80(5)
5 On the Study of Chaotic Systems with Non-Horseshoe Template
85(20)
A. Ray
A. Roy Chowdhury
S. Basak
5.1 Introduction
86(1)
5.2 Formulation
87(3)
5.3 Topological Analysis and Its Invariants
90(2)
5.4 Application to Circuit Data
92(8)
5.4.1 Search for Close Return
92(3)
5.4.2 Topological Constant
95(3)
5.4.3 Template Identification
98(2)
5.4.4 Template Verification
100(1)
5.5 Conclusion and Discussion
100(2)
References
102(3)
6 Instability of Solutions of Fourth and Fifth Order Delay Differential Equations
105(12)
C. Tunc
6.1 Introduction
105(3)
6.2 Open Problems
108(7)
6.3 Conclusion
115(1)
References
115(2)
7 Some Conjectures About the Synchronizability and the Topology of Networks
117(32)
A. Caneco
J. Leonel Rocha
C. Gracio
S. Fernandes
7.1 Introduction
118(3)
7.2 Related and Historical Problems About Network Synchronizability
121(3)
7.3 Some Physical Examples About the Real Applications of Network Synchronizability
124(2)
7.4 Preliminaries
126(2)
7.5 Complete Clustered Networks
128(10)
7.5.1 Clustering Point on Complete Clustered Networks
129(4)
7.5.2 Classification of the Clustering and the Amplitude of the Synchronization Interval
133(3)
7.5.3 Discussion
136(2)
7.6 Symbolic Dynamics and Networks Synchronization
138(6)
References
144(5)
8 Wavelet Study of Dynamical Systems Using Partial Differential Equations
149(6)
E. B. Postnikov
8.1 Definitions and State of Art
149(2)
8.2 Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori
151(1)
8.3 The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case
152(1)
8.4 Discussion of Open Problems
153(1)
References
153(2)
9 Combining the Dynamics of Discrete Dynamical Systems
155(20)
J. S. Canovas
9.1 Introduction
155(3)
9.2 Basic Definitions and Notations
158(3)
9.3 Statement of the Problems
161(11)
9.3.1 Dynamic Parrondo's Paradox and Commuting Functions
163(3)
9.3.2 Dynamics Shared by Commuting Functions
166(2)
9.3.3 Computing Problems for Large Periods T
168(1)
9.3.4 Commutativity Problems
169(2)
9.3.5 Generalization to Continuous Triangular Maps on the Square
171(1)
References
172(3)
10 Code Structure for Pairs of Linear Maps with Some Open Problems
175(20)
P. Troshin
10.1 Introduction
175(1)
10.2 Iterated Function System
176(2)
10.3 Attractor of Pair of Linear Maps
178(1)
10.4 Code Structure of Pair of Linear Maps
179(6)
10.5 Sufficient Conditions for Computing the Code Structure
185(5)
10.6 Conclusion and Open Questions
190(3)
References
193(2)
11 Recent Advances in Open Billiards with Some Open Problems
195(24)
C. P. Dettmann
11.1 Introduction
195(1)
11.2 Closed Dynamical Systems
196(3)
11.3 Open Dynamical Systems
199(5)
11.4 Open Billiards
204(6)
11.5 Physical Applications
210(3)
11.6 Discussion
213(2)
References
215(4)
12 Open Problems in the Dynamics of the Expression of Gene Interaction Networks
219(12)
L. S. Liebovitch
V. Naudot
12.1 Introduction
219(1)
12.2 Attractors for Flows and Diffeomorphisms
220(2)
12.3 Statement of the Problem
222(5)
12.3.1 A First Attempt
222(2)
12.3.2 Examples
224(3)
12.4 Experimental Information
227(1)
12.5 Theoretical Models of Gene Interaction
228(1)
12.6 Conclusions
228(1)
References
229(2)
13 How to Transform a Type of Chaos in Dynamical Systems?
231(22)
E. Zeraoulia
J. C. Sprott
13.1 Introduction
232(1)
13.2 Hyperbolification of Dynamical Systems
232(9)
13.3 Transforming Dynamical Systems to Lorenz-Type Chaos
241(3)
13.4 Transforming Dynamical Systems to Quasi-Attractor Systems
244(2)
13.5 A Common Classification of Strange Attractors of Dynamical Systems
246(1)
References
247(6)
Author Index 253(2)
Subject Index 255
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