Abstract

It is known that small resonant parametric perturbations with a certain phase can stabilize the onset of chaos in a nonlinear system [1]. In this report we show the effects of the resonant perturbations on the whole bifurcation diagram. We demonstrate in experiments with a loss-modulated CO₂ laser that the resonant perturbations produce a phase-dependent stabilizing shift in all bifurcation points. Moreover, they induce bistability in the vicinity of a period-doubling bifurcation (PDB) point. The cavity losses were modulated by the following way: k(t)=k₀+k₁cos(2πft)+k₂ cos(πft +φ), where k₀ is the cavity damping rate due to the cavity losses. The driving signal, k₁cos(2πft), had the frequency f=98 kHz and the amplitude k_t that acted as the bifurcation parameter for our system. The perturbing signal, k₂ cos(πft +<p), at frequency f/2 had an amplitude about 200 times smaller than the driving amplitude at the original chaos threshold. We analyzed the bifurcation diagrams which were obtained by a triangle-shape slow sweeping of the control parameter k₁. By comparing the diagrams obtained by forth and back sweeping of the control parameter k₁ we found hysteresis near the PDB point when the perturbation is added. This means that the resonant perturbation induces bistability in the system. We also observed noise- induced switching between coexisting periodic orbits.

© 1996 IEEE