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 bi...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2016-07, Vol.36, p.517-527
Main Authors: Han, Xiujing, Xia, Fubing, Ji, Peng, Bi, Qinsheng, Kurths, Jürgen
Format: Article
Language:English
Subjects:
Bursting
Circuits
Compound “delayed supHopf/fold cycle-subHopf/supHopf” bursting
Computer simulation
Delay
Hopf bifurcation
Hopf bifurcation delay
Hysteresis loops
Mathematical models
Nonlinearity
“SubHopf/supHopf” bursting via “delayed supHopf/supHopf” hysteresis loop
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Summary:•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.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2016.01.001