Analysis of Asymptotic Solutions to Fuzzy Cellular Automata

Abstract

Abstract. We analyzed asymptotic solutions to fuzzy cellular automata of first order in time with 2 or 3 neighbors in space. The asymptotic solution is a solution evolved after enough time steps from initial value. We proved solutions become uniform or stable asymptotically focusing on one of the following properties; (i) There exist a montonicity on every site. (ii) Lyapunov function exists. (iii) The maximum or minimum values changes monotonicity.