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A cyclic model for gene regulatory networks with time delayed negative feedback is analyzed using an extension of the so-called secant condition, which is originally developed for systems without time delays. It is shown that sufficient conditions obtained earlier for delay-independent local stability can be further improved for homogenous networks to obtain delay-dependent necessary and sufficient conditions, which are expressed in terms of the parameters of the Hill-type nonlinearity.

Analysis of a Gene Regulatory Network Model With Time Delay Using the Secant Condition