Bursting oscillations in Duffing’s equation with slowly changing external forcing

Bursting oscillations with different waveforms can be observed in the forced Duffing’s equation when the external forcing changes slowly. We present an analysis of bursting oscillations by considering the external forcing as a control parameter and studying its influence on the controlled Duffing’s equation. Furthermore, the effects of forcing amplitude γγ and forcing frequency ωω on bursting oscillations are investigated. The forcing amplitude plays an important role in the generation of bursting oscillations, that is, bursting oscillations may be created for γ>239, while if γ<239, they do not occur. On the other hand, the time interval between two adjacent spikes of bursting oscillations is dependent on the forcing frequency, which can be computed at ΔT=πω.

Research highlights
► The forced Duffing’s equation may exhibit bursting oscillations when the external forcing changes slowly.
► We develop two strategies to account for bursting oscillations.
► The forcing amplitude plays an important role in the generation of bursting oscillations.
► The time interval between two adjacent spikes of bursting oscillations is dependent on the forcing frequency.