Abstract
As one of the important artificial oscillatory networks, repressilators have attracted many attentions due to its function of synthesizing oscillations at the cellular level. In this paper, the problem of global exponential stability analysis for nonnegative equilibriums of a delayed coupled repressilator model is addressed. A sufficient condition for the existence of nonnegative equilibrium is first investigated by using the Brouwer’s fixed point theorem. Then a novel approach is proposed to analyze the global exponential stability of nonnegative equilibriums. Thereby, sufficient conditions are derived to guarantee that the considered model has a unique nonnegative equilibrium which is globally exponentially stable. The obtained global exponential stability criteria is only concerned with computing the eigenvalues or the induced norms of a constant matrix, which can be easily verified by using the tool software. The results of an illustrative example present the effect of the proposed approach.
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