Abstract
In this paper, a multi-time-scale-coupled nonlinear dynamic system is constructed by introducing an external excitation into a charge-controlled memcapacitive system. We report the complex bursting oscillation mechanism of this system under different parameter conditions by taking advantage of the fast-slow analysis method. Firstly, we discuss several different types of periodic bursting behaviors consisting of “asymmetric and symmetric ‘delayed pitchfork/Hopf/delayed Homoclinic/Homoclinic/Hopf’ bursting type”, “asymmetric and symmetric ‘delayed Hopf/delayed Homoclinic/Homoclinic/Hopf’ mixed-mode bursting oscillation”, “symmetric ‘delayed Hopf/delayed Homoclinic/delayed pitchfork’ mixed-mode bursting oscillation” and “asymmetric ‘cycle/point’ mixed-mode bursting type via ‘delayed Hopf/delayed pitchfork’ hysteresis loop”. The numerical simulation results express that different delay-bifurcation intervals under the slow passage effect will induce completely various bursting types. Furthermore, we explore a novel route with complex structure from periodic bursting to chaotic bursting. By gradually increasing the value of control parameter, we can observe a variety of dynamic behaviors including complex structure such as symmetric breaking bifurcations, intermittent period-doubling bursting type, period-doubling bifurcations and inverse period-doubling bifurcations. With the further increase of the parameter, the system generates crisis effect, and we can obtain the chaotic attractors in the periodic window. We discover that different parameter conditions can produce chaotic attractors which can induce “‘point/chaos/period/chaos/point’ intermittent chaos type”, “‘point/chaos/point’ intermittent chaos type” and “‘cycle/chaos/cycle’ intermittent chaos type” until complete chaos. Chaotic bursting types are corroborated by the maximum Lyapunov exponents. Our research results enrich the route to bursting oscillation and deepen the understanding of the mechanism of complex bursting oscillation types.
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