Critical and oscillatory behavior of a system of smart preys and predators- art. no. 061907

It is shown that a system of smart preys and predators exhibits irreversibl e phase transitions between a regime of prey-predator coexistence and an st ate where predator extinction is observed. Within the coexistence regime, t he system exhibits a transition between a regime where the densities of spe cies remain constant and another with self-sustained oscillations, respecti vely. 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 the ory. The existence of an oscillatory regime in the thermodynamic limit, whi ch 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.