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Advances in Synchronization of Coupled Fractional Order Systems: Fundamentals and Methods 2018 ed. [Kietas viršelis]

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  • Formatas: Hardback, 185 pages, aukštis x plotis: 235x155 mm, weight: 483 g, 59 Illustrations, color; 7 Illustrations, black and white; XIX, 185 p. 66 illus., 59 illus. in color., 1 Hardback
  • Serija: Understanding Complex Systems
  • Išleidimo metai: 06-Aug-2018
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319939459
  • ISBN-13: 9783319939452
Kitos knygos pagal šią temą:
Advances in Synchronization of Coupled Fractional Order Systems: Fundamentals and Methods 2018 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 185 pages, aukštis x plotis: 235x155 mm, weight: 483 g, 59 Illustrations, color; 7 Illustrations, black and white; XIX, 185 p. 66 illus., 59 illus. in color., 1 Hardback
  • Serija: Understanding Complex Systems
  • Išleidimo metai: 06-Aug-2018
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319939459
  • ISBN-13: 9783319939452
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319939452.html
After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering.





As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few.





This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems. 
1 Introduction
1(10)
1.1 A Brief History of Fractional Calculus
1(2)
1.2 Synchronization, Chaos, and Fractional Calculus
3(8)
1.2.1 Synchronization
3(1)
1.2.2 Chaos
3(1)
1.2.3 Synchronization and Observation
4(1)
1.2.4 Synchronization of Fractional Order Chaotic Systems
5(1)
References
6(5)
2 Basic Concepts and Preliminaries
11(30)
2.1 Gamma Function
11(1)
2.2 Mittagg-Leffler Function
12(1)
2.3 Fractional Operators
13(3)
2.3.1 Riemman-Liouville Fractional Operator
14(1)
2.3.2 Caputo Fractional Operator
14(2)
2.4 Laplace Transform of Fractional Integrals and Fractional Derivatives
16(1)
2.5 Existence and Uniqueness of Fractional Order Systems
17(2)
2.6 Types of Fractional Systems
19(1)
2.7 Algebraic Definitions
20(6)
2.7.1 Commensurate Fractional Order Systems
20(3)
2.7.2 Incommensurate Fractional Order Systems
23(3)
2.8 Stability Results Commensurate Systems
26(12)
2.8.1 Gronwall-Bellman Generalized Lemma
27(5)
2.8.2 Stabilization of Fractional Input-Affine Systems
32(6)
2.9 Stability Result Incommensurate Systems
38(3)
References
38(3)
3 Synchronization of Chaotic Systems by Means of a Nonlinear Observer: An Application to Secure Communications
41(10)
3.1 Introduction
41(1)
3.2 Application Case
42(1)
3.3 Synchronization Methodology
43(3)
3.3.1 Convergence Analysis
45(1)
3.4 Numerical Experiment and Results
46(2)
3.5 Conclusions
48(3)
References
49(2)
4 Synchronization for Chaotic System Through an Observer Using the Immersion and Invariance (I&I) Approach
51(10)
4.1 Preamble
52(1)
4.2 I&I Observer
53(5)
4.3 Numerical Evaluations
58(2)
4.3.1 Duffing's Mechanical Oscillator
58(2)
4.4 Conclusions
60(1)
References
60(1)
5 Synchronization of Nonlinear Fractional-Order Systems by Means of PIrα Reduced Order Observer
61(10)
5.1 Introduction
61(1)
5.2 Problem Statement and Main Result
61(3)
5.3 Numerical Results
64(6)
5.4 Conclusion
70(1)
References
70(1)
6 Estimators for a Class of Commensurate Fractional-Order Systems with Caputo Derivative
71(14)
6.1 Introduction
71(1)
6.2 Problem Formulation
72(1)
6.3 Main Result
73(6)
6.3.1 Fractional-Reduced-Order Observer (FROO)
73(3)
6.3.2 Fractional-Order Luenberger Observer (FLO)
76(3)
6.4 Numerical Examples
79(4)
6.4.1 Fractional-Order Linear Mechanical Oscillator
79(3)
6.4.2 Duffing System
82(1)
6.5 Conclusions
83(2)
References
83(2)
7 Generalized Multi-synchronization of Fractional Order Liouvillian Chaotic Systems Using Fractional Dynamical Controller
85(46)
7.1 Introduction
85(2)
7.2 Problem Formulation
87(7)
7.3 Extension of Results to Complex Interaction Between Slave Systems
94(5)
7.4 Some Numerical Examples
99(24)
7.4.1 Example 1
99(6)
7.4.2 Example 2
105(3)
7.4.3 Example 3
108(7)
7.4.4 Example 4
115(8)
7.5 Concluding Remarks
123(8)
References
129(2)
8 An Observer for a Class of Incommensurate Fractional Order Systems
131(14)
8.1 Introduction
131(1)
8.2 Problem Statement and Main Result
131(3)
8.3 Numerical Results
134(10)
8.4 Conclusions
144(1)
References
144(1)
9 Fractional Generalized Quasi-synchronization of Incommensurate Fractional Order Oscillators
145(16)
9.1 Introduction
145(1)
9.2 Problem Statement and Main Result
146(7)
9.3 Numerical Results
153(5)
9.4 Concluding Remarks
158(3)
References
159(2)
10 Synchronization and Anti-synchronization of Fractional Order Chaotic Systems by Means of a Fractional Integral Observer
161(16)
10.1 Introduction
161(4)
10.1.1 Reduced-Order Fractional Integral Observer
162(1)
10.1.2 Fractional Synchronization Problem
163(2)
10.1.3 Fractional Anti-synchronization Problem
165(1)
10.2 Application to Fractional Chaotic Systems
165(8)
10.2.1 Fractional Lorenz System
165(4)
10.2.2 Fractional Rossler System
169(4)
10.3 Concluding Remarks
173(4)
References
174(3)
Appendix A Integer-Order System 177(4)
Appendix B Fractional-Order System 181(2)
Index 183