Attractor splitting induced by resonant perturbations

We present experimental and numerical results which demonstrate that the so-called nonfeedback control of chaos fundamentally changes the nature of nonautonomous systems. We show that additional weak resonant perturbations (i) induce bistability, splitting the primary attractor into two new ones, and (ii) shift all bifurcation points for these two coexisting attractors in opposite directions as the perturbation amplitude changes. Both perturbation-induced bistability and shift strongly depend on the phase difference between the perturbation and fundamental frequencies. © 1997 The American Physical Society.