Random walk in nonhomogeneous environments: A possible approach to human and animal mobility
arXiv:1702.07561 · doi:10.1103/PhysRevE.95.032133
Abstract
The random walk process in a nonhomogeneous medium, characterised by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. %while the former case resolves itself to a problem with a variable jumping rate, The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.
arXiv comment5 pages, 3 figures
References in corpus (12)
- The scaling laws of human travel
- Modeling the scaling properties of human mobility
- Lévy walks
- Random walks with preferential relocations to places visited in the past and their application to biology
- Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
- Multiplicative Lévy processes: Itô versus Stratonovich interpretation
- Marcus versus Stratonovich for Systems with Jump Noise
- Diffusion equations for a Markovian jumping process
- Nonlinear stochastic equations with multiplicative Lévy noise
- Anomalous diffusion in systems driven by the stable Levy noise with a finite noise relaxation time and inertia
- Anomalous diffusion in nonhomogeneous media: Time-subordinated Langevin equation approach
- Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps