Transition from oscillatory to excitable regime in a system forced at three times its natural frequency - art. no. 056218

The effect of a temporal modulation at three times the critical frequency o n a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from the strong coupling between the external field and the unsta ble modes. We show that, by increasing the intensity of the forcing, one pa sses from an oscillatory regime to an excitable one with three equivalent f requency-locked states. In the oscillatory regime, topological defects are one-armed phase spirals, while in the excitable regime they correspond to t hree-armed excitable amplitude spirals. Analytical results show that the tr ansition between these two regimes occurs at a critical value of the forcin g intensity. The transition between phase and amplitude spirals is confirme d by numerical analysis and it might be observed in periodically forced rea ction-diffusion systems.