Nonequilibrium phase transition of contact processes with the Kauffman NK model

We consider a multistate contact process (CP) in which new particles are created with probabilities that depend on the fitness of the parent particle and with mutations that occur at the time of creation. The fitness is determined by the Kauffman NK model. Using Monte Carlo simulations, we show that such an evolutional CP exhibits critical behaviors that differ from the basic CP. In addition, we present numerical results suggesting that the fitness averaged over surviving particles exhibits a maximum value at the critical point.