Dynamical systems: theories and applications
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2019]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | "A Science Publishers book." |
| Physical Description: | viii, 393 Seiten Illustrationen |
| ISBN: | 9780367137045 0367137046 |
Staff View
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Record in the Search Index
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| adam_text | Contents Preface ui 1. Review of Chaotic Dynamics 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Introduction Poincaré map technique Smale horseshoe Symbolic dynamics Strange attractors Basins of attraction Density, robustness and persistence of chaos Entropies of chaotic attractors Period 3 implies chaos The Snap-back repeller and the Li-Chen-Marotto theorem Shilnikov criterion for the existence of chaos 2. Human Immunodeficiency Virus and Urbanization Dynamics 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Introduction Definition of Human Immunodeficiency Virus (HIV) Modelling the Human Immunodeficiency Virus (HIV) Dynamics of sexual transmission of the Human Immunodeficiency Virus The effects of variable infectivity on the HIV dynamics The CD4+ Lymphocyte dynamics in HIV infection The viral dynamics of a highly pathogenic Simian/Human Immunodeficiency Virus The effects of morphine on Simian Immunodeficiency Viras Dynamics The dynamics of the HIV therapy system Dynamics of urbanization 3. Chaotic Behaviors in Piecewise Linear Mappings 3.1 3.2 3.3 3.4 Introduction Chaos in one-dimensional piecewise smooth maps Chaos in one-dimensional singular maps Chaos in 2-D piecewise smooth maps 1 1 1 3 7 10 13 16 23 32 37 38 46 46 46 48 49 53 56 60 65 67 71 78 78 78 83 86
vi Dynamical Systems: Theories and Applications 4. Robust Chaos in Neural Networks Models 4.1 Introduction 4.2 Chaos in neural networks models 4.3 Robust chaos in discrete time neural networks 4.3.1 Robust chaos in 1 -D piecewise-smooth neural networks 4.3.2 Fragile chaos (blocks with smooth activation function) 4.3.3 Robust chaos (blocks with non-smooth activation fonction) 4.3.4 Robust chaos in the electroencephalogram model 4.3.5 Robust chaos in Diluted circulant networks 4.3.6 Robust chaos in non-smooth neural networks 4.4 The importance of robust chaos in mathematics and some open problems 5. Estimating Lyapunov Exponents of 2-D Discrete Mappings 5.1 Introduction 5.2 Lyapunov exponents of the discrete hyperchaotic double scroll map 5.3 Lyapunov exponents for a class of 2-D piecewise linear mappings 5.4 Lyapunov exponents of a family of 2-D discrete mappings with separate variables 5.5 Lyapunov exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law 5.6 Lyapunov exponents of a modified map-based В VP model 6. Control, Synchronization and Chaotification of Dynamical Systems 6.1 Introduction 6.2 Compound synchronization of different chaotic systems 6.3 Synchronization of 3-D continuous-time quadratic systems using a universal non-linear control law 6.4 Co-existence of certain types of synchronization and its inverse 6.5 Synchronization of 4-D continuous-time quadratic systems using a universal non-linear control law 6.6 Quasi-synchronization of systems with different dimensions 6.7 Chaotification of 3-D linear continuous-time
systems using the signum function feedback 6.8 Chaos control problem of a 3-D cancer model with structured uncertainties 6.9 Controlling homoclinic chaotic attractor 6.10 Robustification of 2-D piecewise smooth mappings 6.11 Chaotifying stable n-D linear maps via the controller of any bounded function 96 96 97 98 101 102 105 109 113 114 115 117 117 117 121 124 128 135 142 142 143 151 155 164 169 173 181 182 186 192
Contents 7. Boundedness of Some Forms of Quadratic Systems 7.1 Introduction 7.2 Boundedness of certain forms of 3-D quadratic continuous-time systems 7.3 Bounded jerky dynamics 7.3.1 Boundedness of general forms of jerky dynamics 7.3.2 Examples of bounded jerky chaos 7.3.3 Appendix A 7.4 Bounded hyperjerky dynamics 7.5 Boundedness of the generalized 4-D hyperchaotic model containing Lorenz-Stenflo and Lorenz-Haken systems 7.5.1 Estimating the bounds for the Lorenz-Haken system 7.5.2 Estimating the bounds for the Lorenz-Stenflo system 7.6 Boundedness of 2-D Hénon-like mapping 7.7 Examples of fully bounded chaotic attractors 8. Some Forms of Globally Asymptotically Stable Attractors 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 Introduction Direct Lyapunov stability for ordinary differential equations Exponential stability of non-linear time-varying Lasalle’s Invariance Principle Direct Lyapunov-type stability for fractional-like systems Construction of globally asymptotically stable n-D discrete mappings Construction of superstable n-D mappings Examples of globally superstable 1-D quadratic mappings Construction of globally superstable 3-D quadratic mappings Hyperbolicity of dynamical systems Consequences of uniform hyperbolicity 8.11.1 Classification of singular-hyperbolic attracting sets Structural stability for 3-D quadratic mappings 8.12.1 The concept of structural stability 8.12.2 Conditions for structural stability 8.12.3 The Jordan normal form Jx 8.12.4 The Jordan normal form J2 8.12.5 The Jordan normal form J3 8.12.6 The Jordan normal form J4 8.12.7
The Jordan normal form J8.12.8 The Jordan normal form,7՜ Construction of globally asymptotically stable partial differential systems Construction of globally stable system of delayed differential equations vii 197 197 197 202 205 214 216 220 224 228 229 233 239 242 242 243 251 259 261 267 271 275 280 285 297 298 302 302 303 306 309 309 310 310 311 312 322
viii Dynamical Systems: Theories and Applications 8.15 Stabilization by the Jurdjevic-Quinn method 8.15.1 The minimization problem 8.15.2 The inverse optimization problem 8.15.3 Input-to-state stability 9. Transformation of Dynamical Systems to Hyperjerky Motions 9.1 Introduction 9.2 Transformation of 3-D dynamical systems to jerk form 9.3 Transformation of 3-D dynamical systems to rational andcubic jerks forms 9.4 Transformation of 4-D dynamical systems to hyperjerkform 9.4.1 The expressionof the transformationbetween (9.45) and (9.61)-(9.62) 9.4.2 Examples of 4-Dhyperjerky dynamics 9.5 Examples of crackle and top dynamics 329 330 331 332 336 336 336 340 343 349 352 359 References 361 Index 389
Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems. Zeraoulia Elhadj, born on February 23, 1976, in Yabous, Khenchela, Algeria, received his B.S. degree in mathematics from the Institute of Mathematics (University of Batna, Batna, Algeria) in 1998 and a Ph.D. degree in mathematics from the University of Constantine, Constantine, Algeria, in 2006. He joined the Department of Mathematics, University of Tébessa, Tébessa, Algeria, in 2001 as a Research Associate, and in the same year, Elhadj became an Assistant Professor. Since 2001, he has been teaching undergraduate and graduate courses on applied mathematics. His primary research interests include bifurcations and chaos. He has authored or coauthored more than 150 journal and conference papers and 15 books. He is the Editor-in-Chief of the Annual Review of Chaos Theory,
Bifurcations and Dynamical Systems Journal. 9780367137045 CRC Press Taylor Francis Group an informa business www.crcpress.com
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| spelling | Zeraoulia, Elhadj 1976- (DE-588)142963844 aut Dynamical systems theories and applications Zeraoulia Elhadj, Department of Mathematics University of Tébessa, Algeria Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2019] © 2019 viii, 393 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier "A Science Publishers book." Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotic behavior in systems Dynamics Dynamisches System (DE-588)4013396-5 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031255267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031255267&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| title | Dynamical systems theories and applications |
| title_auth | Dynamical systems theories and applications |
| title_exact_search | Dynamical systems theories and applications |
| title_full | Dynamical systems theories and applications Zeraoulia Elhadj, Department of Mathematics University of Tébessa, Algeria |
| title_fullStr | Dynamical systems theories and applications Zeraoulia Elhadj, Department of Mathematics University of Tébessa, Algeria |
| title_full_unstemmed | Dynamical systems theories and applications Zeraoulia Elhadj, Department of Mathematics University of Tébessa, Algeria |
| title_short | Dynamical systems |
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| title_sub | theories and applications |
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| topic_facet | Dynamisches System |
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