Frontiers in the study of chaotic dynamical systems with open problems:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2011
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 16 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 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 |
| Beschreibung: | 1 Online-Ressource (viii, 258 p.) |
| ISBN: | 9789814340694 9789814340700 9814340693 9814340707 |
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| 245 | 1 | 0 | |a Frontiers in the study of chaotic dynamical systems with open problems |c edited by Elhadj Zeraoulia, Julien Clinton Sprott |
| 264 | 1 | |a Singapore |b World Scientific |c c2011 | |
| 300 | |a 1 Online-Ressource (viii, 258 p.) | ||
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| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a World Scientific series on nonlinear science |v v. 16 | |
| 500 | |a Includes bibliographical references and indexes | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 650 | 7 | |a SCIENCE / Chaotic Behavior in Systems |2 bisacsh | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Dynamics | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Zeraoulia, Elhadj |e Sonstige |4 oth | |
| 700 | 1 | |a Sprott, Julien C. |e Sonstige |4 oth | |
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| id | DE-604.BV043083530 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:55Z |
| institution | BVB |
| isbn | 9789814340694 9789814340700 9814340693 9814340707 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028507722 |
| oclc_num | 756780625 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (viii, 258 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| series2 | World Scientific series on nonlinear science |
| spelling | Frontiers in the study of chaotic dynamical systems with open problems edited by Elhadj Zeraoulia, Julien Clinton Sprott Singapore World Scientific c2011 1 Online-Ressource (viii, 258 p.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 16 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 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 SCIENCE / Chaotic Behavior in Systems bisacsh Chaotic behavior in systems Dynamics Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Chaotisches System (DE-588)4316104-2 s 1\p DE-604 Zeraoulia, Elhadj Sonstige oth Sprott, Julien C. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389644 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Frontiers in the study of chaotic dynamical systems with open problems SCIENCE / Chaotic Behavior in Systems bisacsh Chaotic behavior in systems Dynamics Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4316104-2 |
| title | Frontiers in the study of chaotic dynamical systems with open problems |
| title_auth | Frontiers in the study of chaotic dynamical systems with open problems |
| title_exact_search | Frontiers in the study of chaotic dynamical systems with open problems |
| title_full | Frontiers in the study of chaotic dynamical systems with open problems edited by Elhadj Zeraoulia, Julien Clinton Sprott |
| title_fullStr | Frontiers in the study of chaotic dynamical systems with open problems edited by Elhadj Zeraoulia, Julien Clinton Sprott |
| title_full_unstemmed | Frontiers in the study of chaotic dynamical systems with open problems edited by Elhadj Zeraoulia, Julien Clinton Sprott |
| title_short | Frontiers in the study of chaotic dynamical systems with open problems |
| title_sort | frontiers in the study of chaotic dynamical systems with open problems |
| topic | SCIENCE / Chaotic Behavior in Systems bisacsh Chaotic behavior in systems Dynamics Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | SCIENCE / Chaotic Behavior in Systems Chaotic behavior in systems Dynamics Dynamisches System Chaotisches System |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=389644 |
| work_keys_str_mv | AT zeraouliaelhadj frontiersinthestudyofchaoticdynamicalsystemswithopenproblems AT sprottjulienc frontiersinthestudyofchaoticdynamicalsystemswithopenproblems |