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Fractional Discrete Chaos: Theories, Methods And Applications [Kietas viršelis]

(Al Zaytoonah University Of Jordan, Jordan), (Ton Duc Thang Univ, Vietnam), (Univ Of Laarbi Tebessi, Algeria)
  • Formatas: Hardback, 220 pages
  • Serija: Topics In Systems Engineering 3
  • Išleidimo metai: 10-Mar-2023
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811271208
  • ISBN-13: 9789811271205
Kitos knygos pagal šią temą:
Fractional Discrete Chaos: Theories, Methods And ApplicationsDidesnis paveikslėlis
  • Formatas: Hardback, 220 pages
  • Serija: Topics In Systems Engineering 3
  • Išleidimo metai: 10-Mar-2023
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811271208
  • ISBN-13: 9789811271205
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789811271205.html
"In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class ofsystems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics. The aims of this book are as follows: Presenting the recent developments, trends, research solutions, applications and open problems related to fractional-order chaotic maps; Illustrating many interdisciplinary applications, like modulization, control, circuits, security and encryption; Including all theories associated with chaos, control and synchronization of discrete-time systems; Providing a useful reference on the topic of fractional-order chaotic maps and their applications"--
Preface ix
Acknowledgment xi
1 Discrete Fractional Calculus
1(34)
1.1 Introduction
1(1)
1.2 Preliminaries
2(2)
1.3 Fractional Difference Operators
4(14)
1.3.1 Fractional Difference Sum Operator
4(4)
1.3.2 Riemann-Liouville Difference Operator
8(5)
1.3.3 Caputo Fractional Difference Operator
13(5)
1.4 Other Fractional Difference Operators
18(4)
1.4.1 Grunwald-Letnikov Fractional Difference Operator
18(1)
1.4.2 Fractional h-Difference Operators
19(3)
1.5 Transform Methods
22(4)
1.5.1 Z-Transform Method
22(2)
1.5.2 Laplace Transform Method
24(2)
1.6 Stability of Fractional Order Difference Systems
26(9)
1.6.1 Stability of Fractional Order Linear Systems
26(6)
1.6.2 Stability of Fractional Order Nonlinear Difference Systems
32(3)
2 Chaotic Methods and Tests
35(26)
2.1 Introduction
35(1)
2.2 Discrete Chaos
36(4)
2.2.1 Characterization of Chaotic Dynamical System
36(1)
2.2.2 Strange Attractor
37(1)
2.2.3 Chaotic Discrete Systems
38(2)
2.3 Classical Tools to Detect Fractional Chaos
40(9)
2.3.1 Bifurcation Diagrams
42(1)
2.3.2 Lyapunov Exponents
43(6)
2.4 0-1 Test Method
49(5)
2.4.1 Applications of the 0-1 Test on Fractional Order Maps
52(2)
2.5 Co Complexity Algorithm
54(3)
2.5.1 Applying Co Complexity for Analyzing the Complexity of Fractional Maps
57(1)
2.6 Approximate Entropy
57(4)
2.6.1 Applying ApEn for Analyzing the Complexity of Fractional Chaotic Duffing Map
60(1)
3 Chaos in 2D Discrete Fractional Systems
61(51)
3.1 Introduction
61(1)
3.2 Fractional Quadratic Maps
62(13)
3.2.1 Fractional-Order Henon Map
63(6)
3.2.2 Fractional Order Flow Map
69(3)
3.2.3 Fractional Order Lorenz Map
72(3)
3.3 Fractional Trigonometric Maps
75(16)
3.3.1 Fractional Order Sine Map
76(8)
3.3.2 Fractional Order Sine-Sine Map
84(7)
3.4 Fractional Rational Maps
91(5)
3.4.1 Fractional Order Rulkov Map
92(3)
3.4.2 Fractional Order Chang et al. Map
95(1)
3.5 Fractional Unified Maps
96(16)
3.5.1 Fractional Order Henon-Lozi Type Map
98(10)
3.5.2 Fractional Order Zeraoulia-Sprott Map
108(4)
4 Chaos in 3D Discrete Fractional Systems
112(60)
4.1 Introduction
112(1)
4.2 Fractional Generalized Henon Map
112(6)
4.3 Fractional Generalized Henon Map with Lorenz-Like Attractors
118(6)
4.3.1 Bifurcation and Chaotic Attractors
120(3)
4.3.2 The 0-1 Test Method
123(1)
4.4 Fractional Stefanski Map
124(5)
4.5 Fractional Rossler System
129(6)
4.6 Fractional Wang Map
135(5)
4.7 Fractional Grassi-Miller Map
140(13)
4.7.1 Dynamics Analysis on Varying a
142(6)
4.7.2 Dynamics Analysis on Varying v
148(2)
4.7.3 The 0-1 Test
150(3)
4.8 Fractional Cournot Game Model
153(19)
4.8.1 The Fractional Order Cournot Game Model with Long Memory
154(2)
4.8.2 Stability Analysis
156(5)
4.8.3 Bifurcation Analysis and Numerical Simulations
161(5)
4.8.4 The 0-1 Test Method
166(1)
4.8.5 Approximate Entropy
167(5)
5 Applications of Fractional Chaotic Maps
172(22)
5.1 Control of Fractional Chaotic Maps
172(9)
5.1.1 Nonlinear Control Laws
173(3)
5.1.2 Linear Control Laws
176(5)
5.2 Synchronization in Fractional Chaotic Maps
181(6)
5.2.1 Generalized Synchronization (GS)
182(1)
5.2.2 Inverse Generalized Synchronization (IGS)
183(1)
5.2.3 Q-S Synchronization
183(1)
5.2.4 The Coexistence of Different Synchronization Types
184(3)
5.3 Encryption Based on Fractional Discrete Chaotic Maps
187(3)
5.3.1 Design of Pseudo-Random Bit Generator (PRBG)
187(2)
5.3.2 Encryption of Electrophysiological Signal
189(1)
5.4 Electronic Implementation of Fractional Chaotic Maps
190(4)
5.4.1 The Fractional Map with the Grunwald-Letnikov Operator
191(2)
5.4.2 Hardware Implementation
193(1)
Bibliography 194(8)
Index 202