Department of Physics, Bar-Ilan University, Ramat Gan, Israel.
Department of Mathematics, Jerusalem College of Technology (JCT), Jerusalem, Israel.
Phys Rev E. 2021 Jan;103(1-1):012114. doi: 10.1103/PhysRevE.103.012114.
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∼S^{4}f^{3/2}.
通过基本模型对觅食行为进行建模是一个最近从多个角度进行研究的问题。然而，人们尚未了解食物在空间中的分布对觅食者寿命的影响。我们在这里探讨了食物在空间中的分布如何在几种不同情况下影响觅食者的寿命。我们在一维和二维中分别分析了随机觅食者和嗅觉觅食者。我们首先考虑一般的食物分布，然后详细分析包括食物之间的恒定距离、每个位置食物存在的特定概率以及食物之间距离的幂律分布在内的特定分布。对于一维中没有嗅觉的觅食者，我们通过分析找到了寿命，对于有嗅觉的觅食者，我们找到了永生的条件。在二维中，我们基于分析考虑发现，寿命（T）与饥饿时间（S）和食物密度（f）的关系为 T∼S^{4}f^{3/2}。
