In this paper, we introduce a class of neutral-type neural networks with delay in the leakage terms. Using coincidence degree theory, Lyapunov functional method and the properties of neutral operator, we establish some new sufficient criteria for the existence and global attractiveness of periodic solutions. Finally, an example demonstrates our findings.

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.

As known, coral reefs have important economic and social value, but they are damaged by various environmental factors worldwide. In this work, a delayed coral reefs system with white noise and L $\acute{e}$vy jumps are studied. First, we examine the existence problem using Lyapunov analysis methods. Then, from a stochastic analysis technique, we studied the problems for the stochastics persistence and extinction. Furthermore, conditions for stochastic bounded in mean were obtained. Our results indicated that large noise intensity was not conducive to populations. The above results may help us better understand the macroalgae and coral reef dynamics in the fluctuating environments. The most important findings of this article are that we studied a variable coefficient coral reef model under various random disturbances and identified the impact of random perturbation and L $\acute{e}$vy jump on the dynamic properties of the system. Finally, five numerical simulations are presented to check the obtained results.