分數(shù)維非線性系統(tǒng)

內容概要

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

作者簡介

作者：（斯洛伐克）帕璀斯 叢書主編：羅朝俊 （瑞典）伊布拉基莫夫

書籍目錄

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

版權頁：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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《分數(shù)維非線性系統(tǒng):建模、分析與仿真(英文版)》是非線性理科學之一。

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