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E-grāmata: Dynamical Systems: Theories and Applications [Taylor & Francis e-book]

(University of Tébessa, Algeria)
  • Formāts: 402 pages, 80 Illustrations, black and white
  • Izdošanas datums: 22-Jan-2019
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429028939
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  • Taylor & Francis e-book
  • Cena: 315,72 €*
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Dynamical Systems: Theories and ApplicationsPalielināt
  • Formāts: 402 pages, 80 Illustrations, black and white
  • Izdošanas datums: 22-Jan-2019
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429028939
Citas grāmatas par šo tēmu:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Rokasgrāmatas mājas lapa: https://www.taylorfrancis.com/books/9780429028939

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.

Preface iii
1 Review of Chaotic Dynamics
1(45)
1.1 Introduction
1(1)
1.2 Poincare map technique
1(2)
1.3 Smale horseshoe
3(4)
1.4 Symbolic dynamics
7(3)
1.5 Strange attractors
10(3)
1.6 Basins of attraction
13(3)
1.7 Density, robustness and persistence of chaos
16(7)
1.8 Entropies of chaotic attractors
23(9)
1.9 Period 3 implies chaos
32(5)
1.10 The Snap-back repeller and the Li-Chen-Marotto theorem
37(1)
1.11 Shilnikov criterion for the existence of chaos
38(8)
2 Human Immunodeficiency Virus and Urbanization Dynamics
46(32)
2.1 Introduction
46(1)
2.2 Definition of Human Immunodeficiency Virus (HIV)
46(2)
2.3 Modelling the Human Immunodeficiency Virus (HIV)
48(1)
2.4 Dynamics of sexual transmission of the Human Immunodeficiency Virus
49(4)
2.5 The effects of variable infectivity on the HIV dynamics
53(3)
2.6 The CD4+ Lymphocyte dynamics in HIV infection
56(4)
2.7 The viral dynamics of a highly pathogenic Simian/Human Immunodeficiency Virus
60(5)
2.8 The effects of morphine on Simian Immunodeficiency Virus Dynamics
65(2)
2.9 The dynamics of the HIV therapy system
67(4)
2.10 Dynamics of urbanization
71(7)
3 Chaotic Behaviors in Piecewise Linear Mappings
78(18)
3.1 Introduction
78(1)
3.2 Chaos in one-dimensional piecewise smooth maps
78(5)
3.3 Chaos in one-dimensional singular maps
83(3)
3.4 Chaos in 2-D piecewise smooth maps
86(10)
4 Robust Chaos in Neural Networks Models
96(21)
4.1 Introduction
96(1)
4.2 Chaos in neural networks models
97(1)
4.3 Robust chaos in discrete time neural networks
98(17)
4.3.1 Robust chaos in 1-D piecewise-smooth neural networks
101(1)
4.3.2 Fragile chaos (blocks with smooth activation function)
102(3)
4.3.3 Robust chaos (blocks with non-smooth activation function)
105(4)
4.3.4 Robust chaos in the electroencephalogram model
109(4)
4.3.5 Robust chaos in Diluted circulant networks
113(1)
4.3.6 Robust chaos in non-smooth neural networks
114(1)
4.4 The importance of robust chaos in mathematics and some open problems
115(2)
5 Estimating Lyapunov Exponents of 2-D Discrete Mappings
117(25)
5.1 Introduction
117(1)
5.2 Lyapunov exponents of the discrete hyperchaotic double scroll map
117(4)
5.3 Lyapunov exponents for a class of 2-D piecewise linear mappings
121(3)
5.4 Lyapunov exponents of a family of 2-D discrete mappings with separate variables
124(4)
5.5 Lyapunov exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law
128(7)
5.6 Lyapunov exponents of a modified map-based BVP model
135(7)
6 Control, Synchronization and Chaotification of Dynamical Systems
142(55)
6.1 Introduction
142(1)
6.2 Compound synchronization of different chaotic systems
143(8)
6.3 Synchronization of 3-D continuous-time quadratic systems using a universal non-linear control law
151(4)
6.4 Co-existence of certain types of synchronization and its inverse
155(9)
6.5 Synchronization of 4-D continuous-time quadratic systems using a universal non-linear control law
164(5)
6.6 Quasi-synchronization of systems with different dimensions
169(4)
6.7 Chaotification of 3-D linear continuous-time systems using the signum function feedback
173(8)
6.8 Chaos control problem of a 3-D cancer model with structured uncertainties
181(1)
6.9 Controlling homoclinic chaotic attractor
182(4)
6.10 Robustification of 2-D piecewise smooth mappings
186(6)
6.11 Chaotifying stable n-D linear maps via the controller of any bounded function
192(5)
7 Boundedness of Some Forms of Quadratic Systems
197(45)
7.1 Introduction
197(1)
7.2 Boundedness of certain forms of 3-D quadratic continuous-time systems
197(5)
7.3 Bounded jerky dynamics
202(18)
7.3.1 Boundedness of general forms of jerky dynamics
205(9)
7.3.2 Examples of bounded jerky chaos
214(2)
7.3.3 Appendix A
216(4)
7.4 Bounded hyperjerky dynamics
220(4)
7.5 Boundedness of the generalized 4-D hyperchaotic model containing Lorenz-Stenflo and Lorenz-Haken systems
224(9)
7.5.1 Estimating the bounds for the Lorenz-Haken system
228(1)
7.5.2 Estimating the bounds for the Lorenz-Stenflo system
229(4)
7.6 Boundedness of 2-D Henon-like mapping
233(6)
7.7 Examples of fully bounded chaotic attractors
239(3)
8 Some Forms of Globally Asymptotically Stable Attractors
242(94)
8.1 Introduction
242(1)
8.2 Direct Lyapunov stability for ordinary differential equations
243(8)
8.3 Exponential stability of non-linear time-varying
251(8)
8.4 Lasalle's Invariance Principle
259(2)
8.5 Direct Lyapunov-type stability for fractional-like systems
261(6)
8.6 Construction of globally asymptotically stable n-D discrete mappings
267(4)
8.7 Construction of superstable n-D mappings
271(4)
8.8 Examples of globally superstable 1-D quadratic mappings
275(5)
8.9 Construction of globally superstable 3-D quadratic mappings
280(5)
8.10 Hyperbolicity of dynamical systems
285(12)
8.11 Consequences of uniform hyperbolicity
297(5)
8.11.1 Classification of singular-hyperbolic attracting sets
298(4)
8.12 Structural stability for 3-D quadratic mappings
302(10)
8.12.1 The concept of structural stability
302(1)
8.12.2 Conditions for structural stability
303(3)
8.12.3 The Jordan normal form J1
306(3)
8.12.4 The Jordan normal form J2
309(1)
8.12.5 The Jordan normal form J3
309(1)
8.12.6 The Jordan normal form J4
310(1)
8.12.7 The Jordan normal form J5
310(1)
8.12.8 The Jordan normal form J6
311(1)
8.13 Construction of globally asymptotically stable partial differential systems
312(10)
8.14 Construction of globally stable system of delayed differential equations
322(7)
8.15 Stabilization by the Jurdjevic-Quinn method
329(7)
8.15.1 The minimization problem
330(1)
8.15.2 The inverse optimization problem
331(1)
8.15.3 Input-to-state stability
332(4)
9 Transformation of Dynamical Systems to Hyperjerky Motions
336(25)
9.1 Introduction
336(1)
9.2 Transformation of 3-D dynamical systems to jerk form
336(4)
9.3 Transformation of 3-D dynamical systems to rational and cubic jerks forms
340(3)
9.4 Transformation of 4-D dynamical systems to hyperjerk form
343(16)
9.4.1 The expression of the transformation between (9.45) and (9.61)-(9.62)
349(3)
9.4.2 Examples of 4-D hyperjerky dynamics
352(7)
9.5 Examples of crackle and top dynamics
359(2)
References 361(28)
Index 389
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.
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