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分数维非线性系统:建模、分析与仿真(英文版)

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分数维非线性系统:建模、分析与仿真(英文版)
出版时间:2011年版
内容简介
  《分数维非线性系统:建模、分析与仿真(英文版)》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。通过学习《分数维非线性系统:建模、分析与仿真(英文版)》,读者可以深入理解分数维微积分的基础理论,快速学会用分数维微分和积分方程来描述动力系统。《分数维非线性系统:建模、分析与仿真(英文版)》可以帮助读者利用分数维混沌系统进一步研究更复杂的物理现象。《分数维非线性系统:建模、分析与仿真(英文版)》可供对混沌现象或分数维系统等感兴趣的数学家、物理学家、工程师参考,也可作为动力系统、控制论和应用数学研究生或本科生的教材。
目录
Introduction
References
2 Fractional Calculus
2.1 Special Functions
2.2 Definitions of Fractional Derivatives and Integrals
2.3 Grtinwald-Letnikov Fractional Integrals and Derivatives
2.4 Riemann-Liouville Fractional Integrals and Derivatives
2.5 Caputo Fractional Derivatives
2.6 Laplace Transform Method
2.6.1 Basic Facts about the Laplace Transform
2.6.2 Laplace Transform of Fractional Integrals
2.6.3 Laplace Transform of Fractional Derivatives
2.7 Fourier Transform Method
2.7.1 Basic Facts about the Fourier Transform
2.7.2 Fourier Transform of Fractional Integrals
2.7.3 Fourier Transform of Fractional Derivatives
2.8 Some Properties of Fractional Derivatives and Integrals
2.9 Numerical Methods for Calculation of Fractional Derivatives and Integrals
2.10 Fractional Calculus and Electricity
2.10.1 Analogue Fractional-Order Circuits
2.10.2 Experimental Measurement
2.10.3 Additional Remarks
References
3 Fractional-Order Systems
3.1 Fractional LTI Systems
3.2 Fractional Nonlinear Systems
3.3 Fractional-Order Controllers
3.3.1 Definition of Fractional-Order Controllers
3.3.2 Properties and Characteristics of Controller
3.3.3 Design of Controller Parameters and Implementation
References
4 Stability of Fractional-Order Systems
4.1 Preliminary Consideration
4.2 Stability of Fractional LTI Systems :
4.3 Stability of Fractional Nonlinear Systems
4.4 Robust Stability of Fractional-Order LTI Systems
4.4.1 Stability Check When the Fractional Orders Are Crisp and Commensurate
4.4.2 Stability Check When the Fractional Orders Are Also Interval Real Numbers
4.5 Stability of Fractional-Order Nonlinear Uncertain Systems
References
5 Fractional-Order Chaotic Systems
5.1 Introduction to Chaotic Dynamics
5.2 Concept of Chuas Circuit
5.2.1 Classical Chuas Oscillator
5.2.2 Fractional-Order Chuas Oscillator
5.2.3 Fractional-Order Chua-Podlubnys Oscillator
5.2.4 Fractional-Order Chua-Hartleys Oscillator
5.2.5 Fractional-Order Memristor-Based Chuas Oscillator
5.3 Fractional-Order Van der Pol Oscillator
5.4 Fractional-Order Duffings Oscillator
5.5 Fractional-Order Lorenzs System
5.6 Fractional-Order Chens System
5.7 Fractional-Order Ltis System
5.8 Fractional-Order Lius System
5.9 Fractional-Order Genesio-Tesis System
5.10 Fractional-Order Arneodos System
5.11 Fractional-Order R6sslers System
5.12 Fractional-Order Newton-Leipniks System
5.13 Fractional-Order Lotka-Volterra System
5.14 Fractional-Order Financial System
5.15 Fractional-Order CNN
5.16 Fractional-Order Voltas System
References
6 Control of Fractional-Order Chaotic Systems
6.1 Preliminary Considerations
6.2 A Survey of Control Strategies
6.3 Examples: Feed-Back Control of Chaotic Systems
6.3.1 Sampled-Data Control of Chuas Oscillator
6.3.2 Sliding Mode Control of the Economical System
References
7 Conclusion
References
Appendix A A List of Matlab Functions
Appendix B Laplace and Inverse Laplace Transforms
Glossary
Index

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