Critical and oscillatory behavior of a system of smart preys and predators

It is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey-predator coexistence and an state where predator extinction is observed. Within the coexistence regime, the system exhibits a transition between a regime where the densities of species remain constant and another with self-sustained oscillations, respectively. This transition is located by means of a combined treatment involving finite-size scaling and Fourier transforms. Furthermore, it is shown that the transition can be rationalized in terms of the standard percolation theory. The existence of an oscillatory regime in the thermodynamic limit, which is in contrast to previous findings of Boccara et al. [Phys. Rev. E 50, 4531 (1994)], may be due to subtle differences between the studied models.