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Published on: May 9, 2021
Two novel bursting patterns in the Duffing system with multiple-frequency slow parametric excitations
Xiujing Han1, Yi Zhang1, Qinsheng Bi1
1Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, People's Republic of China.
Abstract:
This paper aims to report two novel bursting patterns, the turnover-of-pitchfork-hysteresis-induced bursting and the compound pitchfork-hysteresis bursting, demonstrated for the Duffing system with multiple-frequency parametric excitations. Typically, a hysteresis behavior between the origin and non-zero equilibria of the fast subsystem can be observed due to delayed pitchfork bifurcation. Based on numerical analysis, we show that the stable equilibrium branches, related to the non-zero equilibria resulted from the pitchfork bifurcation, may become the ones with twists and turns. Then, the novel bursting pattern turnover-of-pitchfork-hysteresis-induced bursting is revealed accordingly. In particular, we show that additional pitchfork bifurcation points may appear in the fast subsystem under certain parameter conditions. This creates multiple delay-induced hysteresis behavior and helps us to reveal the other novel bursting pattern, the compound pitchfork-hysteresis bursting. Besides, effects of parameters on the bursting patterns are studied to explore the relation of these two novel bursting patterns.
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