Xiaoliang Li

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.

The survival and development of enterprise clusters are closely related to the sustainable development of the entire economy, so research on them has attracted much attention. In this article, we study the dynamic properties of a stochastic enterprise cluster model with high-order perturbation. First, we study stochastically ultimate boundedness of the system. Then, some sufficient condition for the existence of the stationary distribution in the system are obtained. We also discussed the destructiveness and permanence of the system. Finally, three numerical examples are applied to verify the obtained results.

In this note, we investigate the existence and asymptotic property of positive periodic solutions to non-autonomous predator-prey system with stage-structured predator on time scales. Via Schauder’s fixed theorem, easily verifiable sufficient existence conditions of positive periodic solutions for the considered system are obtained. We also study asymptotic property of positive periodic solutions on the basis of existence conditions. Due to the symmetry of periodic solutions, the results of this paper have a certain impact on the study of symmetry. It should be pointed out that the system we are studying is built on arbitrary time scale, so our results generalize the results of existing continuous or discrete systems. Furthermore, we develop Schauder’s fixed theorem for studying the delay system on time scales.

Based on provincial panel data from 2004 to 2022 in China, this article empirically analyzes the nonlinear impact mechanism of agricultural product trade (APT) on agricultural carbon emissions (ACE). The findings are as follows: (1) there is an inverted U-shaped relationship between APT and ACE, which is influenced by the functional areas of food production (The Government of China has designated some provinces as major grain producing areas to guarantee national food security) and the level of fiscal support for agriculture; (2) agricultural technology progress (ATECH) positively regulated the “inverted U” relationship between APT and ACE, accelerated the transition of APT effects on ACE from carbon-increasing to carbon-decreasing, and strengthened the inhibitory effect of APT on ACE in the later stage; (3) further study shows that there was a single rural digitization (RDIG) threshold in the process of APT affecting ACE. That is, after RDIG has crossed the threshold, the inhibitory effect of APT on ACE is more evident. Therefore, this study confirms the significant role of APT in reducing carbon emissions in typical countries, underscoring the importance of strengthening ATECH innovation and promoting RDIG in realizing the environmental greening effect of APT. It also highlights the need to implement tailored APT strategies in different regions.

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.

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive periodic solutions in this paper are general positive functions, not e exponential functions, which generalizes and improves the existing results. We note that due to the symmetrical property of periodic solutions, the results of this paper provide a deeper understanding of the periodic behavior of biological populations. Two numerical examples show the effectiveness of our main results.