Hopf-bifurcation-delay-induced bursting patterns in a modified circuit system

• Two novel Hopf-bifurcation-delay-induced bursting patterns are presented.
• Two factors have been identified as playing decisive roles in the generation of the delay-induced bursting patterns.
• Our results enrich the routes to bursting as well as the underlying mechanisms of bursting.

Based on Hopf bifurcation delay, we present two novel delay-induced bursting patterns in a modified van der Pol-Duffing circuit system. These delay-induced bursting patterns are classified as compound “delayed supHopf/fold cycle-subHopf/supHopf” bursting and “subHopf/supHopf” bursting via “delayed supHopf/supHopf” hysteresis loop, respectively. Our results show that Hopf bifurcation delay plays a decisive role in the generation of these two bursting patterns, which enriches the routes to bursting and deepens the understanding of underlying mechanisms of bursting.