CRITICAL-BEHAVIOR IN COUPLED NONLINEAR-SYSTEMS

We study the critical behavior of period-doubling bifurcations in two coupled one-dimensional maps. In a linear-coupling case, in which the coupling function has a leading linear term, the set of critical points, called the critical set, consists of an infinite number of critical line segments and the zero coupling point, whereas only one critical line segment constitutes the critical set in the case of a nonlinear coupling whose leading term is nonlinear. We find three (two) kinds of critical behaviors in the linear-(nonlinear-) coupling case, depending on the position on the critical set.