Download Long-range Interactions, Stochasticity and Fractional by Albert C. J. Luo, Valentin Afraimovich PDF

By Albert C. J. Luo, Valentin Afraimovich

In reminiscence of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the new advancements of long-range interplay, fractional dynamics, mind dynamics and stochastic concept of turbulence, every one bankruptcy used to be written by way of proven scientists within the box. The publication is devoted to Dr. George Zaslavsky, who was once considered one of 3 founders of the speculation of Hamiltonian chaos. The booklet discusses self-similarity and stochasticity and fractionality for discrete and non-stop dynamical platforms, in addition to long-range interactions and diluted networks. A finished thought for mind dynamics is usually provided. moreover, the complexity and stochasticity for soliton chains and turbulence are addressed. The e-book 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 college Edwardsville, united states. Dr. Valentin Afraimovich is a Professor at San Luis Potosi college, Mexico.

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Extra resources for Long-range Interactions, Stochasticity and Fractional Dynamics: Dedicated to George M. Zaslavsky (1935 - 2008)

Example text

JOY 21t' The integral of this density converges to I for any a i- 0, this means that the Brownian particle sooner or later hits any point x E (-00,00). The Laplace transform of the Smirnov-Levy density is of the form pdA) = la1-:: ["" exp[-At - a2 /(2(j6t)]t - 3/2dt = exp[-(a / (jo)J2I] (jOY 21t' Jo which shows that the case a = 0 is characterized by degenerated D-distribution: 4. Brownian Sample Paths (I) The Brownian particle being at point x = a at time t will with unit probability visit both regions X a and x < a during any small time interval (t, t + h).

24) . 45) . 55) is derived from Eq. 53) , where the dissipation has been introduced into the iteration equation. In this case 16 Vasily E. Tarasov the fractional equation of motion with dissipation is not used. 55) are not derived from fractional differential equations of kicked damped system. We can suggest the second possible getting of a fractional generalization of the Henon map. 35). It is known (see Sect. 56) , I. Using Eq. 58) where T = I, and b = - exp{ -q }. 46) . Proof of this proposition was realized in (Schuster, 1988).

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