Periodic Solution for a Delayed Gene Expression Model

Abstract

In this paper, a modified gene expression model with discrete delays is studied. The oscillatory behavior of the solutions is investigated. Make the change of variables, and the model will be linearized to a time-delayed system. The instability of the trivial solution of the linearized system implies the instability of the equilibrium point of the original model. It will generate a periodic oscillatory solution in which the original system has only one equilibrium point. We extend the result in the literature from stability to oscillation of the model. Some sufficient conditions to guarantee the oscillation of the solutions are provided, and computer simulations are given to support the present result.