A Reaction-Diffusion System of General Gene Expressions with Delays

In this paper, a complete analysis is presented to study a reaction-diffusion system of general gene expressions with two time delays and with Neumann boundary conditions. The global existence of a unique strong solution and the existence of an attractor are established. Using delays as bifurcation parameters, we obtain critical values so that the Hopf bifurcation occurs at the unique equilibrium point. For steady state solutions, the Maximum Principle is used to obtain the bounds of positive solutions. The conditions for the system to have constant are also investigated.