Global stability of delayed genetic regulatory networks with wider hill functions: A mixing monotone semiflows approach.

In this paper, we study the global stability of delayed genetic regulatory networks (DGRNs) with Hill-type activation (or inhibition) functions based on the mixing monotone semiflows approach, where Hill coefficients can be arbitrary positive real number. A new result on the global stability of DGRN is given in the case that all Hill coefficients are less than or equal to 1. In addition, for all Hill coefficients greater than 1, a new sufficient condition for global convergence of DGRN is given, which is less conservative than the condition of the existing correlation results. Finally, two numerical examples and simulations are given to explain the effect of obtained results.