Modeling foraging via basic models is a problem that has been recently investigated from several points of view. However, understanding the effect of the spatial distribution of food on the lifetime of a forager has not been achieved yet. We explore here how the distribution of food in space affects the forager's lifetime in several different scenarios. We analyze a random forager and a smelling forager in both one and two dimensions. We first consider a general food distribution, and then analyze in detail specific distributions including constant distance between food, certain probability of existence of food at each site, and power-law distribution of distances between food. For a forager in one dimension without smell we find analytically the lifetime, and for a forager with sense of smell we find the condition for immortality. In two dimensions we find based on analytical considerations that the lifetime (T) scales with the starving time (S) and food density (f) as T∼S4f3/2.
|Journal||Physical Review E|
|State||Published - Jan 2021|
Bibliographical noteFunding Information:
We thank the Israel Science Foundation (Grant No. 189/19) and the joint China-Israel Science Foundation (Grant No. 3132/19), the BIU Center for Research in Applied Cryptography and Cyber Security, NSF-BSF Grant No. 2019740, and DTRA Grant No. HDTRA-1-19-1-0016 for financial support.
© 2021 American Physical Society.