In this paper, we construct and analyze a stochastic enterprise cluster model with a mean-reverting Ornstein-Uhlenbeck process. We first investigate the existence of a global unique positive solution for the system. After that, the stochastically ultimate boundedness of the system is considered. Based on a series of Lyapunov functions, sufficient criteria for the system's dynamic behaviors, including exponential extinction and persistence in the mean of the system, are established. Two numerical examples validate the theoretical results of this paper. This article provides a theoretical basis for promoting the development of enterprise clusters.

In this work, we study positive periodic solutions of a neutral-type host-macroparasite equation and establish the existence results of positive periodic solutions by using topological degree theory. Furthermore, based on the Lyapunov functional method and differential inequality analysis strategies, the dynamic behaviors of the host-macroparasite model are obtained. Finally, we present a numerical example to verify the effectiveness of the obtained results. It should be pointed out that the properties of neutral operators have significant applications in the proof. Our results have extended existing findings for host-macroparasite equation.

We first study almost periodic solutions of neutral-type differential system on time scales and establish some basic results for the considered system. Furthermore, based on these results, the dynamic behaviors of two classes of neutral-type biological population models including host-macroparasite model and Lasota–Wazewska model are obtained. It is worth mentioning that we study almost periodic solutions for neutral-type differential system on time scales. Furthermore, using the above study and exponential dichotomy method, we investigate two types of biological population models.

This paper aims to study a class of enterprise cluster models with feedback controls and time-varying delays on time scales. Based on periodic time scales theory and the fixed point theorem of strict-set-contraction, some new sufficient conditions for the existence of positive periodic solutions are obtained. Finally, two examples are presented to verify the validity and applicability of the main results in this paper.