A history-dependent stochastic predator-prey model: Chaos and its elimination
Institute for Studies in Theoretical Physics and Mathematics,
PO Box 19395-5531, Tehran, Iran
2 Department of Physics, Sharif University of Technology, PO Box 11365-9161, Tehran, Iran
Published online: 15 February 2000
A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA) and computer simulations. The MFA results a series of bifurcations in the phase space of mean predator and prey densities, leading to a chaotic phase. Because of emerging correlations between the two species distributions, the interaction rate alters and if it is chosen to be the value which is obtained from the simulation, then the chaotic phase disappears.
PACS: 87.23.Cc – Population dynamics and ecological pattern formation / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 82.20.Wt – Computational modeling; simulation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000