I. M. Sokolov

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We propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, cannot be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity(More)
To analyze the role of assortativity in networks we introduce an algorithm which produces assortative mixing to a desired degree. This degree is governed by one parameter p . Changing this parameter one can construct networks ranging from fully random (p=0) to totally assortative (p=1) . We apply the algorithm to a Barabási-Albert scale-free network and(More)
Networks are all around us, from electrical power grids to the biochemistry of cells, from the Internet to social webs. The mathematical concept of network has recently been turned into an important tool for describing complex systems, whose principal characteristic is that they consist of a large number of mutually interacting dynamical parts which are(More)
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability of getting connected to a site at distance d is proportional to d(-alpha), where alpha is a tunable parameter of the model. We show that the properties of(More)
Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for non-Markovian differentiable random processes. We start from an exact expression for the FPT density in terms of an infinite series of integrals over joint densities of level crossings, and consider different approximations based on(More)
Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in(More)
  • I M Sokolov
  • Physical review. E, Statistical, nonlinear, and…
  • 2001
Lévy flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus this process is a kind of continuous-time random walk (CTRW), dual to the typical Scher-Montroll model, in which n grows sublinearly with t. Models in which Lévy flights emerge due to a(More)
To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for the local and concentrations. Their form is rather unusual: The parameters of the reaction influence the diffusion term in the equation for a component A, a(More)
A harmonic oscillator under the influence of noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous. None of these(More)