NDLI: Non-smooth bifurcations on the bursting oscillations in a dynamic system with two timescales

Content Provider	Springer Nature Link
Author	Zhang, Zhengdi Liu, Binbin Bi, Qinsheng
Copyright Year	2014
Abstract	The main purpose of the paper was to explore the structures of bursting oscillations as well as the mechanism of non-smooth dynamic system with two timescales. Based on the typical Chua’s system, a non-smooth dynamic system with two timescales is established, which can be considered as the coupling of slow and fast subsystems. Possible bifurcations as well as the critical conditions related to the equilibrium points of the fast subsystem in different regions divided by the switching boundaries are derived. The distribution of the eigenvalues related to the generalized Jacobian matrix reveals that multiple crossing bifurcations may occur at the switching boundaries, which may influence the dynamics of system. Periodic bursting oscillations can be observed, in which the fold-type non-smooth bifurcations connect the quiescent state and spiking state, leading to the symmetric focus/focus-fold/fold bursting attractors. Different behaviors can be observed at the intersection points between the trajectories and the switching boundaries, which can be explained by the characteristics of the equilibrium points in two regions beside the boundaries. Furthermore, it is found that the real parts of the pair of complex conjugate eigenvalues related to the foci may dramatically depend on certain parameters, which is employed to account for the change in the oscillation patterns related to the spiking state.
Starting Page	195
Ending Page	203
Page Count	9
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	79
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-09-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized Chua’s system Multiple timescales Bursting oscillation Non-smooth bifurcation Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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