CRITICAL-BEHAVIOR OF A PROBABILISTIC CELLULAR-AUTOMATON DESCRIBING A BIOLOGICAL SYSTEM

We study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system. In this model, each site can be occupied by three type of cells and the i mmune response under parasitic infections is described in terms of two parameters p and r. The local rules governing the evolution of this a utomaton possess ''up-down'' symmetry similar to Ising models. Perform ing Monte Carlo simulations on square and cubic lattices we verify tha t the model displays continuous kinetic phase transitions with spontan eous symmetry breaking. We present detailed simulations and analysis o f the critical behavior. Our results indicate that the model belongs t o the Ising universality class, supporting the ''up-down'' conjecture. (C) 1998 Elsevier Science B.V. All rights reserved.