TY - JOUR
A1 - Schwarzl, Maria
A1 - Godec, Aljaz
A1 - Oshanin, Gleb
A1 - Metzler, Ralf
T1 - A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
JF - Journal of physics : A, Mathematical and theoretical
N2 - We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornsteinâ€“Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.
KW - first passage process
KW - diffusion
KW - predator-prey model
Y1 - 2016
U6 - https://doi.org/10.1088/1751-8113/49/22/225601
SN - 1751-8113
SN - 1751-8121
VL - 49
PB - IOP Publ. Ltd.
CY - Bristol
ER -