"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level.   Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

zlibzh/no-category/（斯洛伐克）帕璀斯著, ( si luo fa ke ) pa cui si, Ivo Petrás[著, 帕璀斯, Ivo Petráš/分数维非线性系统 建模、分析与仿真 英文_30419416.pdf

Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation (Nonlinear Physical Science)

Non-Linear System of Fractal Dimension (Modeling Analysis and Simulation) (Chinese Edition)

Fractional order nonlinear systems modeling, analysis and simulation

by Ivo Petráš

Petráš, Ivo

Ivo Petras

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Springer Berlin Heidelberg : Imprint : Springer

Steinkopff. in Springer-Verlag GmbH

Springer-Verlag Berlin Heidelberg

Higher Education Press ; Springer

Springer Nature

Nonlinear Physical Science, Berlin, Heidelberg, Germany, 2011

Nonlinear physical science, Beijing, Berlin, ©2011

Nonlinear Physical Science, 1. ed, Berlin, 2011

Springer Nature, Berlin, Heidelberg, 2011

China, People's Republic, China

Germany, Germany

Bei jing, 2011

1, 20110530

Bookmarks: p1 (p1): 1 Introduction
p2 (p3): References
p3 (p7): 2 Fractional Calculus
p4 (p7): 2.1 Special Functions
p5 (p9): 2.2 Definitions of Fractional Derivatives and Integrals
p6 (p9): 2.3 Grünwald-Letnikov Fractional Integrals and Derivatives
p7 (p11): 2.4 Riemann-Liouville Fractional Integrals and Derivatives
p8 (p12): 2.5 Caputo Fractional Derivatives
p9 (p12): 2.6 Laplace Transform Method
p10 (p12): 2.6.1 Basic Facts about the Laplace Transform
p11 (p14): 2.6.2 Laplace Transform of Fractional Integrals
p12 (p14): 2.6.3 Laplace Transform of Fractional Derivatives
p13 (p15): 2.7 Fourier Transform Method
p14 (p15): 2.7.1 Basic Facts about the Fourier Transform
p15 (p16): 2.7.2 Fourier Transform of Fractional Integrals
p16 (p17): 2.7.3 Fourier Transform of Fractional Derivatives
p17 (p18): 2.8 Some Properties of Fractional Derivatives and Integrals
p18 (p19): 2.9 Numerical Methods for Calculation of Fractional Derivatives and Integrals
p19 (p29): 2.10 Fractional Calculus and Electricity
p20 (p35): 2.10.1 Analogue Fractional-Order Circuits
p21 (p36): 2.10.2 Experimental Measurement
p22 (p37): 2.10.3 Additional Remarks
p23 (p38): References
p24 (p43): 3 Fractional-Order Systems
p25 (p43): 3.1 Fractional LTI Systems
p26 (p47): 3.2 Fractional Nonlinear Systems
p27 (p47): 3.3 Fractional-Order Controllers
p28 (p47): 3.3.1 Definition of Fractional-Order Controllers
p29 (p49): 3.3.2 Properties and Characteristics of Controller
p30 (p51): 3.3.3 Design of Controller Parameters and Implementation
p31 (p52): References
p32 (p55): 4 Stability of Fractional-Order Systems
p33 (p55): 4.1 Preliminary Consideration
p34 (p63): 4.2 Stability of Fractional LTI Systems
p35 (p78): 4.3 Stability of Fractional Nonlinear Systems
p36 (p82): 4.4 Robust Stability of Fractional-Order LTI Systems
p37 (p82): 4.4.1 Stability Check When the Fractional Orders Are Crisp and Commensurate
p38 (p87): 4.4.2 Stability Check When the Fractional Orders Are Also Interval Real Numbers
p39 (p97): 4.5 Stability of Fractional-Order Nonlinear Uncertain Systems
p40 (p98): References
p41 (p103): 5 Fractional-Order Chaotic Systems
p42 (p103): 5.1 Introduction to Chaotic Dynamics
p43 (p104): 5.2 Concept of Chua's Circuit
p44 (p104): 5.2.1 Classical Chua's Oscillator
p45 (p107): 5.2.2 Fractional-Order Chua's Oscillator
p46 (p113): 5.2.3 Fractional-Order Chua-Podlubny's Oscillator
p47 (p114): 5.2.4 Fractional-Order Chua-Hartley's Oscillator
p48 (p114): 5.2.5 Fractional-Order Memristor-Based Chua's Oscillator
p49 (p127): 5.3 Fractional-Order Van der Pol Oscillator
p50 (p130): 5.4 Fractional-Order Duffing's Oscillator
p51 (p134): 5.5 Fractional-Order Lorenz's System
p52 (p138): 5.6 Fractional-Order Chen's System
p53 (p140): 5.7 Fractional-Order Lü's System
p54 (p142): 5.8 Fractional-Order Liu's System
p55 (p145): 5.9 Fractional-Order Genesio-Tesi's System
p56 (p148): 5.10 Fractional-Order Arneodo's System
p57 (p151): 5.11 Fractional-Order R？ssler's System
p58 (p154): 5.12 Fractional-Order Newton-Leipnik's System
p59 (p160): 5.13 Fractional-Order Lotka-Volterra System
p60 (p165): 5.14 Fractional-Order Financial System
p61 (p168): 5.15 Fractional-Order CNN
p62 (p171): 5.16 Fractional-Order Volta's System
p63 (p181): References
p64 (p185): 6 Control of Fractional-Order Chaotic Systems
p65 (p185): 6.1 Preliminary Considerations
p66 (p187): 6.2 A Survey of Control Strategies
p67 (p188): 6.3 Examples:Feed-Back Control of Chaotic Systems
p68 (p188): 6.3.1 Sampled-DataControl of Chua's Oscillator
p69 (p192): 6.3.2 Sliding Mode Control of the Economical System
p70 (p197): References
p71 (p201): 7 Conclusion
p72 (p203): References
p73 (p207): Appendix A A List of Matlab Functions
p74 (p211): Appendix B Laplace and Inverse Laplace Transforms
p75 (p215): Glossary
p76 (p217): Index

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Modeling, Analysis and Simulation presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo PetráS is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of KoSice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics

本书主要讲述分数维混沌系统, 辅以Matlab程序进行仿真, 并用图表展示其状态空间轨迹. 书中对分数维混沌系统的描述清晰, 易懂, 提供的分析方法和数值解法简单易学, 几种典型的分数维系统也用Simulink进行了仿真

Nonlinear Physical Science
Erscheinungsdatum: 30.05.2011

2024-06-13