Levy walk with multiple internal states

Abstract

Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for dealing with the dependence of the PDF of waiting time on the energy of the animal and richness of the food at a particular location, etc; the framework can also be used to model the moving trajectories of smart animals without returning to the directions or locations which they come from immediately. After building the Levy walk model with multiple internal states and deriving the governing equation of the distribution of the positions of the particles, some applications are discussed with specific transition matrices. The type of diffusion for non-immediately-repeating Lévy walk is uncovered, and the distribution and average of first passage time are numerically simulated.

arXiv comment7 pages, 6 figures

References in corpus (5)

• Lévy walks
• Lévy flights versus Lévy walks in bounded domains
• Superdiffusive dispersals impart the geometry of underlying random walks
• Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times
• Fractional compound Poisson processes with multiple internal states

Cited by in corpus (7)

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• Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative
• Aging two-state process with Lévy walk and Brownian motion
• Lévy walk revisited: Hermite polynomial expansion approach
• Numerical algorithm for the space-time fractional Fokker-Planck system with two internal states
• Lévy walk dynamics in non-static media
• Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal states