Dynamic Behavior of a Delayed Model with One Core Enterprise and Four Satellite Enterprises

In this paper, an economic competition–cooperation model is examined, which has one core enterprise and four satellite enterprises. This extends previous smaller models in the literature mathematically. The unique positive solution to the original solution after a change of variables corresponds to a trivial equilibrium of a linearized system. The instability of this linearized solution implies the instability of the positive solution to the original system. The instability of the positive solution and boundedness will force this system to have a periodic solution. Some sufficient conditions to guarantee the periodic oscillation of the solutions for this model are provided, and computer simulations are given to support the present criteria.