Target search by non-Brownian stochastic processes

4 July 2019, 3.45 PM - 4 July 2019, 4.30 PM

Rainer Klages

Queen Mary University of London, UK

I consider three generic types of stochastic processes that are important to model target search, say, by a biological forager. The first one is search in a field of targets by fractiomal Brownian motion. Computer simulations show an intricate dependence of the search efficiency on basic physical quantities like the density of targets, the perception radius of the searcher and the average displacement of the searcher [1]. The second class of processes is Lévy flights and walks. Simulation results on first passage and first arrival times for a single target, partially supported by analytical arguments, highlight the difference between finite and infinite velocity processes [2]. Thirdly, I comment on the formal relation between Lévy walks and Poisson-Kac processes, the latter defining Gaussian finite velocity processes. Clarifying this connection leads to new, more general finite velocity processes with potential relevance to foraging theory [3].

[1] S.M.J.Khadem, S.H.L.Klapp, R.Klages, tbp

[2] V.V.Palyulin, G.Blackburn, M.A.Lomholt, N.W.Watkins, R.Metzler, R.Klages, A.V.Chechkin, submitted

[3] M.Giona, A.Cairoli, R.Klages, tbp

 

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