Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

Abstract

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

“…The sufficient conditions which ensure the existence and stability of unique globally attractive periodic solution of the system without time delays are established. The obtained results are completely new and complement the published works of [25][26][27][28][29]46].…”

“…In this paper, we consider the permanence and periodic solutions of two enterprises with multiple delays, which is more general than those models in [46]. Thus our results complement the previous work of [46].…”

“…Although Zhi et al [46] have investigated the permanence and almost periodic solution for an enterprise cluster model based on ecology theory with feedback controls on time scales, they also do not consider the enterprise cluster model with time delays, moveover, they do not investigate the periodic solution of this model. In this paper, we consider the permanence and periodic solutions of two enterprises with multiple delays, which is more general than those models in [46]. Thus our results complement the previous work of [46].…”

Nabla inequalities and permanence for a logistic integrodifferential equation on time scales

“…A distributed delay has been proposed to describe the population growth of some species, which can date back to the works of Volterra [17,18,19]. Up to now, literature has focused on permanence of ecosystems on time scales, see [20,21]. However, to the best of the authors' knowledge, there are few papers studying the permanence of ecosystem with distributed delays on time scales.…”

Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

“…In recent years, a variety of dynamic equations on time scales have been investigated (see [1,2,3,4,5,6,11,12,17]). However, only few papers [7,15,16] published on the permanence for dynamic equation models on time scales, and up to now, there is no paper published on the permanence for impulsive dynamic equation models on time scales. Thus, it is worthwhile continuing to study the single-species system with impulsive effects on time scales.…”