Study of interacting particle systems: the transition to the oscillatory behavior of a prey–predator model

A prey–predator system with intelligent pursuit and evasion is studied by means of computer simulations. It is found that the model exhibits a coexistence state between prey and predators. In this state and depending on the parameters, the system may evolve toward two different regimes, characterized by the behavior of the prey–predator population. Whitin the oscillatory (fixed point) regime the specieʹs density changes periodically (remains constant), respectively. The transition between such regimes is rationalized in terms of a dynamic percolation process.