ON CRITICAL PHENOMENA IN INTERACTING GROWTH SYSTEMS .2. BOUNDED GROWTH

This paper completes the classification of some infinite and finite growth systems which was started in Part I. Components whose states are integer numbers interact in a local deterministic way, in addition to which every component's state grows by a positive integer k with a probability epsilon(k)(1 - epsilon) at every moment of the discrete time. Proposition 1 says that in the infinite system which starts from the state ''all zeros,'' percentages of elements whose states exceed a given value k greater-than-or-equal-to 0 never exceed (Cepsilon)k, where C = const. Proposition 2 refers to finite systems. It states that the same inequalities hold during a time which depends exponentially on the system size.