Dynamics of bow-tie shaped bursting: Forced pendulum with dynamic feedback

Publication Type:

Journal Article

Source:

Chaos: An interdisciplinary Journal of Nonlinear Science, Volume 26 , Issue 123107 (2016)

URL:

http://scitation.aip.org/content/aip/journal/chaos/26/12/10.1063/1.4971411

Abstract:

A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this forced system with dynamic feedback. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state. The resting period between two successive bursts (Trest) is estimated analytically.