2018/06/04 by Yuquan Chen, Derek Hollenbeck, Chen, Yuquan +5
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1806.00909
openalex publication_date 2018/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal random foraging strategy has gained increasing concentrations. It is shown that Lévy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard Lévy flight generally cannot be followed in practice. In this paper, we assume that each flight of the forager is possibly interrupted by some uncertain factors, such as obstacles on the flight direction, natural enemies in the vision distance, and restrictions in the energy storage for each flight, and introduce the tempered Lévy distribution p(l)∼ \rm e-ρll-μ. It is validated by both theoretical analyses and simulation results that a higher searching efficiency can be derived when a smaller ρ or μ is chosen. Moreover, by taking the flight time as the waiting time, the master equation of the random searching procedure can be obtained. Interestingly, we build two different types of master equations: one is the standard diffusion equation and the other one is the tempered fractional diffusion equation.