The present study examines the dynamical behaviors and the mechanism of a modified van der Pol–Duffing circuit system with slow-varying periodic excitation. Based on the analysis of the equilibrium states, the stable equilibrium and limit cycle oscillation are found to switch as the parameter slowly varies. The periodic and bursting oscillations are observed as the parameter slowly varies within the different parameter regions, especially one type of Hopf-bifurcation-delay-induced bursting oscillation. These Hopf-bifurcation-delay-induced bursting patterns are studied in detail, thereby generating compound classifications, namely “delayed supHopf/fold cycle-subHopf/supHopf” bursting and “subHopf/supHopf” bursting via “delayed supHopf/ supHopf” hysteresis loop.
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