By Albert C. J. Luo, Valentin Afraimovich
In reminiscence of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the hot advancements of long-range interplay, fractional dynamics, mind dynamics and stochastic conception of turbulence, each one bankruptcy was once written by way of proven scientists within the box. The ebook is devoted to Dr. George Zaslavsky, who used to be one in every of 3 founders of the speculation of Hamiltonian chaos. The e-book discusses self-similarity and stochasticity and fractionality for discrete and non-stop dynamical platforms, in addition to long-range interactions and diluted networks. A complete thought for mind dynamics is additionally provided. moreover, the complexity and stochasticity for soliton chains and turbulence are addressed. The publication is meant for researchers within the box of nonlinear dynamics in arithmetic, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois collage Edwardsville, united states. Dr. Valentin Afraimovich is a Professor at San Luis Potosi college, Mexico.
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Additional resources for Long-range Interactions, Stochasticity and Fractional Dynamics: Dedicated to George M. Zaslavsky (1935 - 2008)
This type of motion can be considered as a fractional generalization of chaotic attractor. As a result , I Fractional Zaslavsky and Henon Discrete Maps 25 the fractional discrete maps allow to study a new type of attractors that are called pseudochaotic. 7 Conclusion In many areas of mechanics and physics the problems can be reduced to the study of discrete maps. In particular the special case of discrete maps has been studied to describe properties of regular and strange attractors . Under a wide range of circumstances such maps give rise to chaotic behavior.
Phys. A , 41, 435101. , 1978, Simplest case of a strange attractor, Phys. Let. A, 69, 145147. , 2005, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford. A. , 2006, Chaotic and pseudochaotic attractors of perturbed fractional oscillator, Chaos, 16,013102. M . , Superdiffusion in the di ssipative standard map, Chaos, 18,033116. l952). Chapter 2 Self-similarity, Stochasticity and Fractionality Vladimir V. Uchaikin Abstract Self-similar generalizations of Brownian motion, Levy motion, Poisson process and compound Poisson process are considered.
The term of a periodic sequence of delta-function type pulses (kicks). The other generalization that is described by Eq. 20) is suggested in (Tarasov and Zaslavsky, 2008). The discrete map that corresponds to the suggested 17 I Fractional Zaslavsky and Henon Discrete Maps fractional equation of order 0 :::; f3 < 1 is derived . This map can be considered as a generalization of univers al map for the case 0 < f3 < I. 9) in the form (0 :::;f3 <1) . x(-r) oD I x-oIl Dl x - r(1 _ f3) Jo (t - -r)/3 ct:r ' c /3 _ (0 :::; f3 < 1).