title: Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback.
abstract: Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.
authors.affiliation: Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.
authors.forename: Pushpita
authors.initials: P
authors.lastname: Ghosh
authors.forename: Shrabani
authors.initials: S
authors.lastname: Sen
authors.forename: Syed Shahed
authors.initials: SS
authors.lastname: Riaz
authors.forename: Deb Shankar
authors.initials: DS
authors.lastname: Ray
mesh_terms: D005246:Feedback; D017711:Nonlinear Dynamics; D010507:Periodicity; D013997:Time Factors