Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Abstract

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

A memristive non-smooth dynamical system with coexistence of bimodule periodic oscillation

“…Then, Qu et al [22] further investigated a more complex double excitation non-smooth Filippov system and discovered the multi-sliding bifurcation oscillation phenomenon. And Zhang et al [23] found that introducing a non-smooth factor into the chaotic geomagnetic field model can lead to the phenomenon of grazingsliding bifurcation and cross-sliding bifurcation. In addition, Leutcho et al [24,25] studied chaotic hyperjerk circuits and revealed the phenomenon of mixed-mode bursting oscillations and various coexisting Feigenbaum remerging trees.…”

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

“…e introduction of the slow-fast dynamics analysis method [19] well explained the bifurcation connection between the spiking state and the quiescent state, so as the mechanism of bursting oscillation. Based on this method, various bursting oscillation modes [20][21][22][23][24][25][26][27][28][29][30][31][32][33] are obtained, such as fold/fold bursting and fold/ Hopf bursting. In nonlinear dynamical system, two time scales can lead to complex dynamical behavior of the system, so it is widely concerned by academic circles domestically and overseas.…”

Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

“…Li et al [53] presented an algorithm for computing 2D stable and unstable manifolds of hyperbolic fixed points of nonlinear maps, and its performance was demonstrated by hyperchaotic 3D Hénon map and Lorenz system. Zhang et al [54] and Han et al [55] discussed the dynamical behaviors of bursting oscillations. Zhang et al [56] studied the existence and stability of the Hopf bifurcation of a modified Pan-like chaotic system.…”