Complex behavior of fuzzy logistic rule 90 automaton
A dynamical system falling in between the elementary binary cellular automata and the coupled map lattices is presented. It is composed by a one-dimensional cellular automaton in which the values within each cell are continuous instead of discrete. However, in this case, the coupling between cells is made through a logistic map instead of making the fuzzification of the disjunctive normal form describing the corresponding Boolean rule. The system resembles the CA rule 90 evolution, since the future value of a cell depends only on a combination of the values of the nearest neighbors cells. The basic dynamical and stability properties of the system are analyzed. The system displays different types from attractors (fixed points, cycles and chaotic attractors), depending on the growth rate parameter used for the logistic map coupling. If the cell values are binary, i.e., only values 0 and 1 are allowed within each cell, the dynamical evolution of the rule 90 automaton is recovered.
logistic rule 90 chaotic behavior fuzzy cellular automata