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Zbl 1242.34058
Bi, Qinsheng; Zhang, Zhengdi
Bursting phenomena as well as the bifurcation mechanism in controlled Lorenz oscillator with two time scales. (English)
[J] Phys. Lett., A 375, No. 8, 1183-1190 (2011). ISSN 0375-9601

Summary: A controlled Lorenz model with fast-slow effect has been established, in which there exist order gap between the variables associated with the controller and the original Lorenz oscillator, respectively. The conditions of fold bifurcation as well as Hopf bifurcation for the fast subsystem are derived to investigate the mechanism of the behaviors of the whole system. Two cases in which the equilibrium points of the fast subsystem behave in different characteristics have been considered, leading to different dynamical evolutions with the change of coupling strength. Several types of bursting phenomena, such as fold/fold burster, fold/Hopf burster, near-fold/Hopf burster, fold/near-Hopf buster have been observed. Theoretical analysis shows that the bifurcations points which connect the quiescent state and the repetitive spiking state agree well with the turning points of the trajectories of the bursters. Furthermore, the mechanism of the period-adding bifurcations, resulting in the rapid change of the period of the movements, is presented.

MSC 2000:: *34C15 Nonlinear oscillations of solutions of ODE
34C23 Bifurcation (periodic solutions)

Keywords: quiescent state; spiking; bursting; bifurcation mechanism

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