Global asymptotical stability of a unique almost periodic solution for enterprise clusters based on ecology theory with time-varying delays and feedback controls

Abstract

This paper is concerned with some dynamic behavior of enterprises cluster constituted by n satellite enterprises and a dominant enterprise. We present a model involving time-varying delays and feedback controls based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environments. Applying the comparison theorem of differential equations and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotically stable nonnegative almost periodic solution of the system are obtained. Finally, we present an example to explain the economical significance of mathematical results.