American Research Journal of Mathematics

In this paper, the oscillatory behavior of the solutions for a coupled Stuart-Landau oscillator model with delays is investigated. Time delay induced partial death patterns with conjugate coupling in relay oscillators has been investigated in the literature which is very special case because this model includes only one delay. According to the practical problem, the propagation delays are not the same as one. A model includes six different time delays is considered. By mathematical analysis method, the oscillatory behavior of the Stuart-Landau oscillators is brought to the instability of a unique equilibrium point of the model and the boundedness of the solutions. Some sufficient conditions to guarantee the existence of oscillatory 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 time delays affect the oscillatory frequency much and amplitude slightly