Periodic oscillation for a coupled ring Stuart-Landau oscillators
Abstract
In this paper, the existence of periodic oscillation of the solutions for a coupled ring
Stuart-Landau oscillators model with delays is investigated. Double Hopf bifurcation of coupled
dissipative Stuart-Landau oscillators with delay has been investigated in the literature which is
very special case because this model considered only one delay. A model includes n different
time delays is considered. By the extended Chafee’s criterion, the oscillatory behavior of the
Stuart-Landau oscillators model is brought to the instability of the unique equilibrium point
and the boundedness of the solutions of the system. Some sufficient conditions to guarantee the
oscillation of the solutions which are very easy to check comparing to the bifurcating method
are provided. Computer simulations are given to support the present results. Our simulation
suggests that synchronization phenomenon occurred, and time delays affect the oscillatory
frequency much and amplitude slightly.
Keywords: coupled ring Stuart-Landau oscillator, delay, instability, oscillation
