Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

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.

5 pages, 3 figures

References in corpus (6)

• The scaling laws of human travel
• Lévy walks
• Random walks with preferential relocations to places visited in the past and their application to biology
• Marcus versus Stratonovich for Systems with Jump Noise
• Anomalous diffusion in nonhomogeneous media: Time-subordinated Langevin equation approach
• Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps

Cited by in corpus (1)

• First-passage and first-hitting times of Levy flights and Levy walks