Analysis of a gene regulatory network model with time delay using the secant condition

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 suf cient conditions obtained earlier for delay-independent local stability can be further improved for homogenous networks to obtain delay-dependent necessary and suf cient conditions, which are expressed in terms of the parameters of the Hill-type nonlinearity.