长距离相互作用.随机及分数维动力学 节选

《长距离相互作用、随机及分数维动力学》内容简介：In memory of Dr. George Zaslavsky, Long-range Interactions, Stochasticity and Fractional Dynamics covers'the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering.

长距离相互作用.随机及分数维动力学 相关资料

插图：Note that the continuous limit of discrete systems with power-law long-range interactions gives differential equations with derivatives of non-integer orders with respect to coordinates （Tarasov and Zaslavsky, 2006; Tarasov, 2006）. Fractional differentiation with respect to time is characterized by long-term memory effects that correspond to intrinsic dissipative processes in the physical systems. The memory effects to discrete maps mean that their present state evolution depends on all past states. The discrete maps with memory are considered in the papers （Fulinski and Kleczkowski, 1987;Fick et al., 1991; Giona, 1991; Hartwich and Fick, 1993; Gallas, 1993; Stanislavsky,2006; Tarasov and Zaslavsky, 2008; Tarasov, 2009; Edelman and Tarasov, 2009）.The interesting question is a connection of fractional equations of motion and thediscrete maps with memory. This derivation is realized for universal and standard maps in （Tarasov and Zaslavsky, 2008; Tarasov, 2009）. It is important to derive discrete maps with memory from equations of motion with fractional derivatives. It was shown （Zaslavsky et al., 2006） that perturbed by aperiodic force, the nonlinear system with fractional derivative exhibits a new type of chaotic motion called the fractional chaotic attractor.

长距离相互作用.随机及分数维动力学 作者简介

编者：罗朝俊 （墨西哥）阿弗莱诺维奇（Valentin Afraimovich） 丛书主编：（瑞典）伊布拉基莫夫Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville,USA.Dr. Valentin Afraimovich is a Proiessor at San Luis Potosi University, Mexico.

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自然科学 数学 概率论与数理统计

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