Oscillatory Behavior for a coupled Stuart - Landau Oscillator Model with delays

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Chunhua Feng^*

Citation: Chunhua Feng ”Oscillatory behavior for a coupled Stuart-Landau oscillator model with delays”. American Research Journal of Mathematics, vol 6, no. 1, 2020, pp. 1-10.

Copyright Copyright © 2020 Feng C, This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract:

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.

Key words: Coupled Stuart-Landau oscillator, delay, instability, oscillation

Description:

INTRODUCTION

It is well known that the coupled dynamical systems with time-delays arise in various applications
including semiconductor lasers [1-3], electronic circuits [4], optoelectronic oscillators [5],
mechanical system [6, 7], neuronal networks [8-13], socioeconomic systems [14], and many
others [15-24]. Recently, Sharma has investigated the following delay-coupled
Stuart-Landau oscillators [25]:

CONCLUSION

In this paper, we have discussed the oscillatory behavior of the solutions for a coupled Stuart-Landau oscillator
model with delays. Based on mathematical analysis method, we provided some sufficient conditions to guarantee
the existence of oscillatory solutions. Some simulations are provided to indicate the correction of the criteria.

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