On systems of rational difference equations and periodic tetrachotomies

Abstract

We study the following system of two rational difference equationswith nonnegative parameters and nonnegative initial conditions. We assume that B j = C j = D j = E j = 0 for j = k, 2k, 3k, . . . and establish the existence of periodic tetrachotomy behavior which depends on a 2 × 2 matrix with entries β k , γ k , δ k , and ǫ k .