Phase diagram of a cyclic predator-prey model by the gradient method

MAURICIO GIRARDI; NARA GUISONI

Vienna

Conferencia; ECCS'11 Vienna European Conference on Complex Systems; 2011

European Conference on Complex Systems

In this work we study a cyclic predator-prey model in a square lattice by Monte Carlo simulations with the recently introduced gradient method [E.S. Loscar et al. PRE, 80, 051123 (2009)]. Here each site is empty or occupied by a single specie labeled as 1, . . . , n, and the system evolves through the invasion of preys sites by neighboring predators with the cyclic rule 1 → 2 → 3 . . . → 1, and by the site exchange of neutral pairs. Due to the exchange and invasion rules, the number of entities are conserved. This model presents irreversible phase transitions from active to absorbing phases were only odd or even species survive depending on the system parameters. The control parameters are the invasion and the exchange rates which, in our case, are considered as a gradient in the horizontal axis of the lattice. This gradient allows the presence of both active and absorbing phases separated by an interface which we used to determine the loci of phase transitions. By the characterization of these interfaces, one can determine the universality class and the order of the active-absorbing transition. We can also define an interface between percolating and no-percolating phases. For the case of four species and no empty site, we constructed the system’s phase diagram and obtained the critical exponents of the transitions. We studied n > 4 and the presence of empty sites, that also induces to phase transition by increasing the rate of neutral pairs exchange.