Local Stability of Positive Almost Periodic Solutions for an Enterprise Cluster Model with Feedback Controls

In this paper, a non-autonomous enterprise cluster model with feedback controls is investigated. Some new criteria for analyzing the existence and local stability of positive almost periodic solutions are proposed. Methods including coincidence degree theory, Lyapunov method and inequality techniques are used in the present paper. In particular, by means of coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions of the system. Based on Lyapunov stability theory, local stability of positive almost periodic solutions is obtained. To illustrate the applicability and validity of Theorems 1 and 2, a numerical example is presented. It is interesting that almost periodic solutions possess a certain degree of symmetry.