AUTHOR=Chen Yuquan , Hollenbeck Derek , Wang Yong , Chen YangQuan 

TITLE=On Optimal Tempered Lévy Flight Foraging

JOURNAL=Frontiers in Physics

VOLUME=Volume 6 - 2018

YEAR=2018

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00111

DOI=10.3389/fphy.2018.00111

ISSN=2296-424X

ABSTRACT=Optimal random foraging strategy has gained increasing attention. It is shown that L{\'e}vy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard L{\'e}vy 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 L{\'e}vy distribution $p(l)\sim {\rm e}^{-\rho l}l^{-\mu}$. It is validated by both theoretical analyses and simulation results that a higher searching efficiency can be achieved when a smaller $\rho$ or $\mu$ 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.