Multistability in a driven nonlinear system controlled by weak subharmonic perturbations

It is shown that weak resonant perturbations at sub-harmonic frequencies can induce and control multi-stability in a wide class of nonlinear systems, which display the period doubling route into chaos or possess isolated subharmonic branches. The number of attractors induced depends on the subharmonic frequency, amplitude and phase of periodic perturbations as well as an initial dynamical state of nonlinear systems. Besides, phase scaling relations for the onsets of both saddle-node bifurcations and boundary crises induced by resonant periodic perturbations at subharmonic frequencies are found from the numerical simulation. These phase dependences determine the domains of existence of induced attractors in (bifurcation parameter, perturbation phase) parameter space. The overlapping of these domains leads to the formation of zones with different number of coexisting attractors. Experimental and numerical evidences are given on the basis of a loss-modulated CO₂ laser.