Occurrence of multiple period-doubling bifurcation route to chaos in periodically pulsed chaotic dynamical systems

Abstract

We consider the effect of discrete-time signal or periodically pulsed forcing on chaotic dynamical systems and show that the systems can undergo novel multiple period-doubling bifurcations prior to the onset of chaos, followed by a rich variety of dynamical phenomena including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures and so on. Under certain circumstances, these systems also admit transcritical bifurcations preceding the onset of multiple period-doubling bifurcations. These properties are demonstrated for the case of Duffing oscillator. We also explain the occurrence of multiple period-doubling by means of a periodically forced logistic map.