分?jǐn)?shù)維非線性系統(tǒng)

內(nèi)容概要

　　本書(shū)主要講述分?jǐn)?shù)維混沌系統(tǒng)，輔以Matlab程序進(jìn)行仿真，并用圖表展示其狀態(tài)空間軌跡。書(shū)中對(duì)分?jǐn)?shù)維混沌系統(tǒng)的描述清晰、易懂，提供的分析方法和數(shù)值解法簡(jiǎn)單易學(xué)，幾種典型的分?jǐn)?shù)維系統(tǒng)也用Simulink進(jìn)行了仿真。通過(guò)學(xué)習(xí)本書(shū)，讀者可以深入理解分?jǐn)?shù)維微積分的基礎(chǔ)理論，快速學(xué)會(huì)用分?jǐn)?shù)維微分和積分方程來(lái)描述動(dòng)力系統(tǒng)。本書(shū)可以幫助讀者利用分?jǐn)?shù)維混沌系統(tǒng)進(jìn)一步研究更復(fù)雜的物理現(xiàn)象。
　　本書(shū)可供對(duì)混沌現(xiàn)象或分?jǐn)?shù)維系統(tǒng)等感興趣的數(shù)學(xué)家、物理學(xué)家、工程師參考，也可作為動(dòng)力系統(tǒng)、控制論和應(yīng)用數(shù)學(xué)研究生或本科生的教材。

作者簡(jiǎn)介

作者：（斯洛伐克）帕璀斯 叢書(shū)主編：羅朝俊 （瑞典）伊布拉基莫夫

書(shū)籍目錄

1　Introduction
2　Fractional Calculus
3　Fractional-Order Systems
4　Stabilify of Fractional-Order Systems
5　Fractional-Order Chaotic Systems
6　Control of Fractional-Order Chaotic Systems
7　Conclusion
Appendix A　A List of Matlab Functions
AppendixB　Laplace and Inverse Laplace Transforms
Glossary
Index

章節(jié)摘錄

版權(quán)頁(yè)：插圖：It is well known that chaos cannot occur in continuous nonlinear systems with the total order less than three (Silva, 1993). This assertion is based on the usual concepts of order, such as the number of states in a system or the total number of separate differentiations or integrations in the system. The model of chaotic system can be rearranged to three single differential equations, where the equations contain the non-integer (fractional) order derivatives. The total order of the system is the sum of each particular order instead of three. To put this fact into context, we can consider the fractional-order dynamical model of the system. Hartley et al. introduced the fractional-order Chua's system (Hartley et al., 1995). In the work (Arena et al., 1998), the fractional-order cellular neural network (CNN) was considered, the fractional Duffing's system was presented in the work (Gao and Yu, 2005), while other fractional-order chaotic systems were described in many other works (e.g., Ahmad, 2005; Deng et al., 2007; Guo, 2005; Li and Chen, 2004; Lu, 2005a,b; Nimmo and Evans, 1999, etc.). In all these cases chaos was exhibited in a system with total order less than three.

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