The Existence of Periodic Solutions for a Two-Enterprise Interaction Model with Delays

Various enterprise interaction models with or without time delays appeared in the literature. The stability and Hopf bifurcation for one or two delays in the models were studied by many researchers. However, the periodic oscillation for a four time delays enterprise interaction model is still an open problem due to the complexity of the bifurcating equation. In this paper, by means of the mathematical analysis method, some sufficient conditions to guarantee the existence of periodic oscillatory solution for the four time delays model are obtained. An open problem is solved. Computer simulation is given to demonstrate the present results.