Bursting Oscillation Structures and Dynamical Mechanics in Two Frequency Scales
Journal Title: 河南科技大学学报（自然科学版） - Year 2017, Vol 38, Issue 4
Abstract
A non-autonomous Duffing-van der Pol oscillator was taken as an example to explore the fast and slow coupling effects of different frequency scales, when there was a magnitude gap between the external forcing frequency and the natural frequency of the system. The stabilities and bifurcation behaviors of the fast subsystem were analyzed to obtain corresponding two-parameter bifurcation sets by fixing the slow forcing term.The bifurcation sets were divided into five areas, and the bursting oscillation patterns related to each area were analyzed. The bursting behaviers of point-point type ( e. g., symmetric fold/fold bursting and symmetric sub Hopf/sub Hopf bursting) and the bursting patterns of point-cycle type ( e. g., symmetric sub Hopf/fold cycle bursting and symmetric delayed sup Hopf/delayed sup Hopf bursting) were revealed. The results show that the coexistence of multiple solutions and multiple bifurcations of the fast subsystem plays a vital role in theinduction of various symmetric bursting oscillation patterns.
Authors and Affiliations
Fubing XIA, Xiujing HAN, Rui QU, Qinsheng BI
Keywords
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