Frontiers in the study of chaotic dynamical systems with open problems /:
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...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific,
©2011.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Special theme issues and proceedings ;
v. 16. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (viii, 258 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9789814340700 9814340707 |
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| 245 | 0 | 0 | |a Frontiers in the study of chaotic dynamical systems with open problems / |c edited by Elhadj Zeraoulia, Julien Clinton Sprott. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific, |c ©2011. | ||
| 300 | |a 1 online resource (viii, 258 pages) : |b illustrations | ||
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| 490 | 1 | |a World Scientific series on nonlinear science. Series B. Special theme issues and proceedings ; |v v. 16 | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 505 | 0 | 0 | |g Machine generated contents note: |g 1. |t Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / |r Y. Lin -- |g 1.1. |t Introduction -- |g 1.2. |t Lorenz's Modeling and Problems of the Model -- |g 1.3. |t Computational Schemes and What Lorenz's Chaos Is -- |g 1.4. |t Discussion -- |g 1.5. |t Appendix: Another Way to Show that Chaos Theory Suffers From Flaws -- |t References -- |g 2. |t Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / |r L.S. Yao -- |g 2.1. |t Introduction -- |g 2.2. |t Open Problems About Nonexistence of Chaotic Solutions -- |t References -- |g 3. |t Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / |r J. Heidel -- |g 3.1. |t First Open Problem -- |g 3.2. |t Second Open Problem -- |g 3.3. |t Third Open Problem -- |g 3.4. |t Fourth Open Problem -- |g 3.5. |t Fifth Open Problem -- |g 3.6. |t Sixth Open Problem -- |t References -- |g 4. |t On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / |r G.M. Mahmoud. |
| 505 | 0 | 0 | |g 4.1. |t Introduction -- |g 4.2. |t Examples -- |g 4.2.1. |t Dynamical Properties of Chaotic Complex Chen System -- |g 4.2.2. |t Hyperchaotic Complex Lorenz Systems -- |g 4.3. |t Open Problems -- |g 4.4. |t Conclusions -- |t References -- |g 5. |t On the Study of Chaotic Systems with Non-Horseshoe Template / |r S. Basak -- |g 5.1. |t Introduction -- |g 5.2. |t Formulation -- |g 5.3. |t Topological Analysis and Its Invariants -- |g 5.4. |t Application to Circuit Data -- |g 5.4.1. |t Search for Close Return -- |g 5.4.2. |t Topological Constant -- |g 5.4.3. |t Template Identification -- |g 5.4.4. |t Template Verification -- |g 5.5. |t Conclusion and Discussion -- |t References -- |g 6. |t Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / |r C. Tunc -- |g 6.1. |t Introduction -- |g 6.2. |t Open Problems -- |g 6.3. |t Conclusion -- |t References -- |g 7. |t Some Conjectures About the Synchronizability and the Topology of Networks / |r S. Fernandes -- |g 7.1. |t Introduction -- |g 7.2. |t Related and Historical Problems About Network Synchronizability -- |g 7.3. |t Some Physical Examples About the Real Applications of Network Synchronizability. |
| 505 | 0 | 0 | |g 7.4. |t Preliminaries -- |g 7.5. |t Complete Clustered Networks -- |g 7.5.1. |t Clustering Point on Complete Clustered Networks -- |g 7.5.2. |t Classification of the Clustering and the Amplitude of the Synchronization Interval -- |g 7.5.3. |t Discussion -- |g 7.6. |t Symbolic Dynamics and Networks Synchronization -- |t References -- |g 8. |t Wavelet Study of Dynamical Systems Using Partial Differential Equations / |r E.B. Postnikov -- |g 8.1. |t Definitions and State of Art -- |g 8.2. |t Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori -- |g 8.3. |t The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case -- |g 8.4. |t Discussion of Open Problems -- |t References -- |g 9. |t Combining the Dynamics of Discrete Dynamical Systems / |r J.S. Canovas -- |g 9.1. |t Introduction -- |g 9.2. |t Basic Definitions and Notations -- |g 9.3. |t Statement of the Problems -- |g 9.3.1. |t Dynamic Parrondo's Paradox and Commuting Functions -- |g 9.3.2. |t Dynamics Shared by Commuting Functions. |
| 505 | 0 | 0 | |g 9.3.3. |t Computing Problems for Large Periods T -- |g 9.3.4. |t Commutativity Problems -- |g 9.3.5. |t Generalization to Continuous Triangular Maps on the Square -- |t References -- |g 10. |t Code Structure for Pairs of Linear Maps with Some Open Problems / |r P. Troshin -- |g 10.1. |t Introduction -- |g 10.2. |t Iterated Function System -- |g 10.3. |t Attractor of Pair of Linear Maps -- |g 10.4. |t Code Structure of Pair of Linear Maps -- |g 10.5. |t Sufficient Conditions for Computing the Code Structure -- |g 10.6. |t Conclusion and Open Questions -- |t References -- |g 11. |t Recent Advances in Open Billiards with Some Open Problems / |r C.P. Dettmann -- |g 11.1. |t Introduction -- |g 11.2. |t Closed Dynamical Systems -- |g 11.3. |t Open Dynamical Systems -- |g 11.4. |t Open Billiards -- |g 11.5. |t Physical Applications -- |g 11.6. |t Discussion -- |t References -- |g 12. |t Open Problems in the Dynamics of the Expression of Gene Interaction Networks / |r V. Naudot -- |g 12.1. |t Introduction -- |g 12.2. |t Attractors for Flows and Diffeomorphisms. |
| 505 | 0 | 0 | |g 12.3. |t Statement of the Problem -- |g 12.3.1. |t A First Attempt -- |g 12.3.2. |t Examples -- |g 12.4. |t Experimental Information -- |g 12.5. |t Theoretical Models of Gene Interaction -- |g 12.6. |t Conclusions -- |t References -- |g 13. |t How to Transform a Type of Chaos in Dynamical Systems? / |r J.C. Sprott -- |g 13.1. |t Introduction -- |g 13.2. |t Hyperbolification of Dynamical Systems -- |g 13.3. |t Transforming Dynamical Systems to Lorenz-Type Chaos -- |g 13.4. |t Transforming Dynamical Systems to Quasi-Attractor Systems -- |g 13.5. |t A Common Classification of Strange Attractors of Dynamical Systems -- |t References. |
| 588 | 0 | |a Print version record. | |
| 520 | |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 | 0 | |a Chaotic behavior in systems. |0 http://id.loc.gov/authorities/subjects/sh85022562 | |
| 650 | 0 | |a Dynamics. |0 http://id.loc.gov/authorities/subjects/sh85040316 | |
| 650 | 6 | |a Chaos. | |
| 650 | 6 | |a Dynamique. | |
| 650 | 7 | |a SCIENCE |x Chaotic Behavior in Systems. |2 bisacsh | |
| 650 | 7 | |a Chaotic behavior in systems |2 fast | |
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| 700 | 1 | |a Zeraoulia, Elhadj. |4 edt | |
| 700 | 1 | |a Sprott, Julien C. |4 edt | |
| 776 | 0 | 8 | |i Print version: |t Frontiers in the study of chaotic dynamical systems with open problems. |d Singapore ; Hackensack, N.J. : World Scientific, ©2011 |z 9814340693 |w (OCoLC)697261743 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series B, |p Special theme issues and proceedings ; |v v. 16. |0 http://id.loc.gov/authorities/names/n94078562 | |
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| author_additional | Y. Lin -- L.S. Yao -- J. Heidel -- G.M. Mahmoud. S. Basak -- C. Tunc -- S. Fernandes -- E.B. Postnikov -- J.S. Canovas -- P. Troshin -- C.P. Dettmann -- V. Naudot -- J.C. Sprott -- |
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| contents | Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / Introduction -- Lorenz's Modeling and Problems of the Model -- Computational Schemes and What Lorenz's Chaos Is -- Discussion -- Appendix: Another Way to Show that Chaos Theory Suffers From Flaws -- References -- Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / Open Problems About Nonexistence of Chaotic Solutions -- Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / First Open Problem -- Second Open Problem -- Third Open Problem -- Fourth Open Problem -- Fifth Open Problem -- Sixth Open Problem -- On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / Examples -- Dynamical Properties of Chaotic Complex Chen System -- Hyperchaotic Complex Lorenz Systems -- Open Problems -- Conclusions -- On the Study of Chaotic Systems with Non-Horseshoe Template / Formulation -- Topological Analysis and Its Invariants -- Application to Circuit Data -- Search for Close Return -- Topological Constant -- Template Identification -- Template Verification -- Conclusion and Discussion -- Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / Conclusion -- Some Conjectures About the Synchronizability and the Topology of Networks / Related and Historical Problems About Network Synchronizability -- Some Physical Examples About the Real Applications of Network Synchronizability. Preliminaries -- Complete Clustered Networks -- Clustering Point on Complete Clustered Networks -- Classification of the Clustering and the Amplitude of the Synchronization Interval -- Symbolic Dynamics and Networks Synchronization -- Wavelet Study of Dynamical Systems Using Partial Differential Equations / Definitions and State of Art -- Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori -- The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case -- Discussion of Open Problems -- Combining the Dynamics of Discrete Dynamical Systems / Basic Definitions and Notations -- Statement of the Problems -- Dynamic Parrondo's Paradox and Commuting Functions -- Dynamics Shared by Commuting Functions. Computing Problems for Large Periods T -- Commutativity Problems -- Generalization to Continuous Triangular Maps on the Square -- Code Structure for Pairs of Linear Maps with Some Open Problems / Iterated Function System -- Attractor of Pair of Linear Maps -- Code Structure of Pair of Linear Maps -- Sufficient Conditions for Computing the Code Structure -- Conclusion and Open Questions -- Recent Advances in Open Billiards with Some Open Problems / Closed Dynamical Systems -- Open Dynamical Systems -- Open Billiards -- Physical Applications -- Open Problems in the Dynamics of the Expression of Gene Interaction Networks / Attractors for Flows and Diffeomorphisms. Statement of the Problem -- A First Attempt -- Experimental Information -- Theoretical Models of Gene Interaction -- How to Transform a Type of Chaos in Dynamical Systems? / Hyperbolification of Dynamical Systems -- Transforming Dynamical Systems to Lorenz-Type Chaos -- Transforming Dynamical Systems to Quasi-Attractor Systems -- A Common Classification of Strange Attractors of Dynamical Systems -- References. |
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Postnikov --</subfield><subfield code="g">8.1.</subfield><subfield code="t">Definitions and State of Art --</subfield><subfield code="g">8.2.</subfield><subfield code="t">Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori --</subfield><subfield code="g">8.3.</subfield><subfield code="t">The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case --</subfield><subfield code="g">8.4.</subfield><subfield code="t">Discussion of Open Problems --</subfield><subfield code="t">References --</subfield><subfield code="g">9.</subfield><subfield code="t">Combining the Dynamics of Discrete Dynamical Systems /</subfield><subfield code="r">J.S. 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Naudot --</subfield><subfield code="g">12.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">12.2.</subfield><subfield code="t">Attractors for Flows and Diffeomorphisms.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">12.3.</subfield><subfield code="t">Statement of the Problem --</subfield><subfield code="g">12.3.1.</subfield><subfield code="t">A First Attempt --</subfield><subfield code="g">12.3.2.</subfield><subfield code="t">Examples --</subfield><subfield code="g">12.4.</subfield><subfield code="t">Experimental Information --</subfield><subfield code="g">12.5.</subfield><subfield code="t">Theoretical Models of Gene Interaction --</subfield><subfield code="g">12.6.</subfield><subfield code="t">Conclusions --</subfield><subfield code="t">References --</subfield><subfield code="g">13.</subfield><subfield code="t">How to Transform a Type of Chaos in Dynamical Systems? /</subfield><subfield code="r">J.C. 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| id | ZDB-4-EBA-ocn756780625 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:02Z |
| institution | BVB |
| isbn | 9789814340700 9814340707 |
| language | English |
| oclc_num | 756780625 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (viii, 258 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Special theme issues and proceedings ; |
| series2 | World Scientific series on nonlinear science. Series B. Special theme issues and proceedings ; |
| spelling | Frontiers in the study of chaotic dynamical systems with open problems / edited by Elhadj Zeraoulia, Julien Clinton Sprott. Singapore ; Hackensack, N.J. : World Scientific, ©2011. 1 online resource (viii, 258 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series on nonlinear science. Series B. Special theme issues and proceedings ; 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. Print version record. 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. Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Chaos. Dynamique. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast Zeraoulia, Elhadj. edt Sprott, Julien C. edt Print version: Frontiers in the study of chaotic dynamical systems with open problems. Singapore ; Hackensack, N.J. : World Scientific, ©2011 9814340693 (OCoLC)697261743 World Scientific series on nonlinear science. Series B, Special theme issues and proceedings ; v. 16. http://id.loc.gov/authorities/names/n94078562 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389644 Volltext |
| spellingShingle | Frontiers in the study of chaotic dynamical systems with open problems / World Scientific series on nonlinear science. Special theme issues and proceedings ; Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / Introduction -- Lorenz's Modeling and Problems of the Model -- Computational Schemes and What Lorenz's Chaos Is -- Discussion -- Appendix: Another Way to Show that Chaos Theory Suffers From Flaws -- References -- Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / Open Problems About Nonexistence of Chaotic Solutions -- Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / First Open Problem -- Second Open Problem -- Third Open Problem -- Fourth Open Problem -- Fifth Open Problem -- Sixth Open Problem -- On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / Examples -- Dynamical Properties of Chaotic Complex Chen System -- Hyperchaotic Complex Lorenz Systems -- Open Problems -- Conclusions -- On the Study of Chaotic Systems with Non-Horseshoe Template / Formulation -- Topological Analysis and Its Invariants -- Application to Circuit Data -- Search for Close Return -- Topological Constant -- Template Identification -- Template Verification -- Conclusion and Discussion -- Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / Conclusion -- Some Conjectures About the Synchronizability and the Topology of Networks / Related and Historical Problems About Network Synchronizability -- Some Physical Examples About the Real Applications of Network Synchronizability. Preliminaries -- Complete Clustered Networks -- Clustering Point on Complete Clustered Networks -- Classification of the Clustering and the Amplitude of the Synchronization Interval -- Symbolic Dynamics and Networks Synchronization -- Wavelet Study of Dynamical Systems Using Partial Differential Equations / Definitions and State of Art -- Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori -- The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case -- Discussion of Open Problems -- Combining the Dynamics of Discrete Dynamical Systems / Basic Definitions and Notations -- Statement of the Problems -- Dynamic Parrondo's Paradox and Commuting Functions -- Dynamics Shared by Commuting Functions. Computing Problems for Large Periods T -- Commutativity Problems -- Generalization to Continuous Triangular Maps on the Square -- Code Structure for Pairs of Linear Maps with Some Open Problems / Iterated Function System -- Attractor of Pair of Linear Maps -- Code Structure of Pair of Linear Maps -- Sufficient Conditions for Computing the Code Structure -- Conclusion and Open Questions -- Recent Advances in Open Billiards with Some Open Problems / Closed Dynamical Systems -- Open Dynamical Systems -- Open Billiards -- Physical Applications -- Open Problems in the Dynamics of the Expression of Gene Interaction Networks / Attractors for Flows and Diffeomorphisms. Statement of the Problem -- A First Attempt -- Experimental Information -- Theoretical Models of Gene Interaction -- How to Transform a Type of Chaos in Dynamical Systems? / Hyperbolification of Dynamical Systems -- Transforming Dynamical Systems to Lorenz-Type Chaos -- Transforming Dynamical Systems to Quasi-Attractor Systems -- A Common Classification of Strange Attractors of Dynamical Systems -- References. Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Chaos. Dynamique. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85022562 http://id.loc.gov/authorities/subjects/sh85040316 |
| title | Frontiers in the study of chaotic dynamical systems with open problems / |
| title_alt | Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine / Introduction -- Lorenz's Modeling and Problems of the Model -- Computational Schemes and What Lorenz's Chaos Is -- Discussion -- Appendix: Another Way to Show that Chaos Theory Suffers From Flaws -- References -- Nonexistence of Chaotic Solutions of Nonlinear Differential Equations / Open Problems About Nonexistence of Chaotic Solutions -- Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems / First Open Problem -- Second Open Problem -- Third Open Problem -- Fourth Open Problem -- Fifth Open Problem -- Sixth Open Problem -- On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems / Examples -- Dynamical Properties of Chaotic Complex Chen System -- Hyperchaotic Complex Lorenz Systems -- Open Problems -- Conclusions -- On the Study of Chaotic Systems with Non-Horseshoe Template / Formulation -- Topological Analysis and Its Invariants -- Application to Circuit Data -- Search for Close Return -- Topological Constant -- Template Identification -- Template Verification -- Conclusion and Discussion -- Instability of Solutions of Fourth and Fifth Order Delay Differential Equations / Conclusion -- Some Conjectures About the Synchronizability and the Topology of Networks / Related and Historical Problems About Network Synchronizability -- Some Physical Examples About the Real Applications of Network Synchronizability. Preliminaries -- Complete Clustered Networks -- Clustering Point on Complete Clustered Networks -- Classification of the Clustering and the Amplitude of the Synchronization Interval -- Symbolic Dynamics and Networks Synchronization -- Wavelet Study of Dynamical Systems Using Partial Differential Equations / Definitions and State of Art -- Open Problems in the Continuous Wavelet Transform and a Topology of Bounding Tori -- The Evaluation of the Continuous Wavelet Transform Using Partial Differential Equations in Non-Cartesian Co-ordinates and Multidimensional Case -- Discussion of Open Problems -- Combining the Dynamics of Discrete Dynamical Systems / Basic Definitions and Notations -- Statement of the Problems -- Dynamic Parrondo's Paradox and Commuting Functions -- Dynamics Shared by Commuting Functions. Computing Problems for Large Periods T -- Commutativity Problems -- Generalization to Continuous Triangular Maps on the Square -- Code Structure for Pairs of Linear Maps with Some Open Problems / Iterated Function System -- Attractor of Pair of Linear Maps -- Code Structure of Pair of Linear Maps -- Sufficient Conditions for Computing the Code Structure -- Conclusion and Open Questions -- Recent Advances in Open Billiards with Some Open Problems / Closed Dynamical Systems -- Open Dynamical Systems -- Open Billiards -- Physical Applications -- Open Problems in the Dynamics of the Expression of Gene Interaction Networks / Attractors for Flows and Diffeomorphisms. Statement of the Problem -- A First Attempt -- Experimental Information -- Theoretical Models of Gene Interaction -- How to Transform a Type of Chaos in Dynamical Systems? / Hyperbolification of Dynamical Systems -- Transforming Dynamical Systems to Lorenz-Type Chaos -- Transforming Dynamical Systems to Quasi-Attractor Systems -- A Common Classification of Strange Attractors of Dynamical Systems -- References. |
| 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 | Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Chaos. Dynamique. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast |
| topic_facet | Chaotic behavior in systems. Dynamics. Chaos. Dynamique. SCIENCE Chaotic Behavior in Systems. Chaotic behavior in systems Dynamics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=389644 |
| work_keys_str_mv | AT zeraouliaelhadj frontiersinthestudyofchaoticdynamicalsystemswithopenproblems AT sprottjulienc frontiersinthestudyofchaoticdynamicalsystemswithopenproblems |