title: Dynamics of bow-tie shaped bursting: Forced pendulum with dynamic feedback.
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.
authors.affiliation: Centre for Complex Systems and Soft Matter Physics, International Institute of Information Technology, Bangalore (IIIT-B), 26/C Electronics City, Hosur Road, Bangalore 560100, India.
authors.forename: Thotreithem
authors.initials: T
authors.lastname: Hongray
authors.affiliation: School of Natural Sciences and Engineering, National Institute of Advanced Studies (N.I.A.S.), Indian Institute of Science Campus, Bangalore 560012, India.
authors.forename: Janaki
authors.initials: J
authors.lastname: Balakrishnan