Oscillatory Behavior for an Enterprise Cluster Model with Multiple Delays

In this paper, a competition-cooperation enterprise cluster model with delays is studied. The oscillatory behavior of the solutions is investigated. We extend the result in the literature from a mathematical point of view. Make the change of variables and deal with the instability of linearized system. The boundedness of the solutions of the system and the instability of the unique positive equilibrium point will force the system to generate a periodic solution around the equilibrium. Two sufficient conditions to guarantee the periodic oscillation of the solutions are provided based on the instability of the equilibrium point, and computer simulations are given to support the present criteria.