长距离相互作用.随机及分数维动力学 本书特色

《长距离相互作用、随机及分数维动力学》：Nonlinear Physical Science focuses on the recent advances of fundamental theories and principles, analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications.

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 目录

1 fractional zaslavsky and henon discrete maps
vasily e. tarasov
1.1 introduction
1.2 fractional derivatives
1.2.1 fractional riemann-liouville derivatives
1.2.2 fractional caputo derivatives
1.2.3 fractional liouville derivatives
1.2.4 interpretation of equations with fractional derivatives.
1.2.5 discrete maps with memory
1.3 fractional zaslavsky maps
1.3.1 discrete chirikov and zaslavsky maps
1.3.2 fractional universal and zaslavsky map
1.3.3 kicked damped rotator map
1.3.4 fractional zaslavsky map from fractional differential equations
1.4 fractional h6non map
1.4.1 henon map
1.4.2 fractional henon map
1.5 fractional derivative in the kicked term and zaslavsky map
1.5.1 fractional equation and discrete map
1.5.2 examples
1.6 fractional derivative in the kicked damped term and generalizations of zaslavsky and henon maps
1.6.1 fractional equation and discrete map
1.6.2 fractional zaslavsky and henon maps
1.7 conclusion
references
2 self-similarity, stochasticity and fractionality
vladimir v uchaikin
2.1 introduction
2.1.1 ten years ago
2.1.2 two kinds of motion
2.1.3 dynamic self-similarity
2.1.4 stochastic self-similarity
2.1.5 self-similarity and stationarity
2.2 from brownian motion to levy motion
2.2.1 brownian motion
2.2.2 self-similar brownian motion in nonstationary nonhomogeneous environment
2.2.3 stable laws
2.2.4 discrete time levy motion
2.2.5 continuous time levy motion
2.2.6 fractional equations for continuous time levy motion
2.3 fractional brownian motion
2.3.1 differential brownian motion process
2.3.2 integral brownian motion process
2.3.3 fractional brownian motion
2.3.4 fractional gaussian noises
2.3.5 barnes and allan model
2.3.6 fractional levy motion
2.4 fractional poisson motion
2.4.1 renewal processes
2.4.2 self-similar renewal processes
2.4.3 three forms of fractal dust generator
2.4.4 nth arrival time distribution
2.4.5 fractional poisson distribution
2.5 fractional compound poisson process
2.5.1 compound poisson process
2.5.2 levy-poisson motion
2.5.3 fractional compound poisson motion
2.5.4 a link between solutions
2.5.5 fractional generalization of the levy motion
acknowledgments
appendix. fractional operators
references
3 long-range interactions and diluted networks
antonia ciani, duccio fanelli and stefano ruffo

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