Global synchronization of coupled genetic oscillators with distributed delay

In this paper, the synchronization problem for the collective dynamics among genetic oscillators with distributed delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having distributed delay. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be synchronized. The criteria obtained in this paper are in the form of matrix inequalities.