Universality of period doubling in coupled maps

초록

We study the critical behavior of period doubling in two coupled one-dimensional maps with a single maximum of order z. In particular, the effect of the maximum-order z on the critical behavior associated with coupling is investigated by a renormalization method. There exist three fixed maps of the period-doubling renormalization operator. For a fixed map associated with the critical behavior at the zero-coupling critical point, relevant eigenvalues associated with coupling perturbations vary, depending on the order z, whereas they are independent of z for the other two fixed maps. The renormalization results for the zero-coupling case are also confirmed by a direct numerical method. © 1994 The American Physical Society.