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《分數維非線性系統(建模、分析與仿真)》(作者帕璀斯)主要講述分數維混沌系統，輔以Matlab程序進行仿真，并用圖表展示其狀態空間軌跡。書中對分數維混沌系統的描述清晰、易懂，提供的分析方法和數值解法簡單易學，幾種典型的分數維系統也用Simulink進行了仿真。通過學習《分數維非線性系統(建模、分析與仿真)》，讀者可以深入理解分數維微積分的基礎理論，快速學會用分數維微分和積分方程來描述動力系統。《分數維非線性系統(建模、分析與仿真)》可以幫助讀者利用分數維混沌系統進一步研究更復雜的物理現象。 《分數維非線性系統(建模、分析與仿真)》可供對混沌現象或分數維系統等感興趣的數學家、物理學家、工程師參考，也可作為動力系統、控制論和應用數學研究生或本科生的教材。
目次
1 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
