On the critical behavior of a lattice prey-predator model

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolation like transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward infinite number of absorbing states, and the corresponding steady-state exponents are mean-field like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. The use of dynamical Monte-Carlo method shows that a particular strategy for preparing the initial state should be devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.