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This paper studies a stochastic two-species Schoener's competitive model with Lévy jumps by the mean-reverting Ornstein–Uhlenbeck process. First, the biological implication of introducing the Ornstein–Uhlenbeck process is illustrated. After that, we show the existence and uniqueness of the global solution. Moment estimates for the global solution of the stochastic model are then given. Moreover, by constructing the Lyapunov function and applying Itô's formula and Chebyshev's inequality, it is found that the model is stochastic and ultimately bounded. In addition, we give sufficient conditions for the extinction of species. Finally, numerical simulations are employed to demonstrate the analytical results.

In this work, we set up a new discrete predator-prey competitive model with time-varying delays and feedback controls. By virtue of the difference inequality knowledge, a sufficient condition which guarantees the permanence of the established discrete predator-prey competitive model with time-varying delays and feedback controls is derived. Under some appropriate parameter conditions, we have proved that the periodic solution of the system without delay exists and globally attractive. To verify the correctness of the derived theoretical fruits, we give two examples and execute computer simulations. Our obtained results are novel and complement previous known results.

Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.

This paper examines a three-species ecological competition model with two predators and one prey, incorporating food-limited growth and both linear and quadratic harvesting strategies. Using mathematical analysis, we identify equilibrium points and derive conditions for their stability and persistence. The results reveal that quadratic harvesting significantly enhances stability, promotes coexistence, and mitigates extinction risks compared to linear harvesting. Numerical simulations validate the theoretical findings, highlighting the effectiveness of quadratic harvesting in managing population dynamics. These insights contribute to the mathematical understanding of sustainable harvesting strategies in complex ecological systems.

In this paper, based on a guanaco–sheep competitive system, we develop and analyze mathematical models with unilateral and bilateral control for the management of overgrazing. We first analyze the dynamics of the uncontrolled system. It then follows the analysis of the system with impulsive control by differential equation geometry theory. We mainly prove the existence and stability of order-1 periodic solution for unilateral control system and order-2 periodic solution for bilateral control system. Some numerical simulations including the bifurcation diagrams of periodic solution are carried out, which not only verify the validity of the theoretical results, but also reveal some special dynamic phenomena, such as the appearance of higher-order periodic solutions and the existence of parameter intervals with the order change of periodic solution. Comparing the unilateral and bilateral control strategy, we encourage bilateral control rather than unilateral control for the management of sheep species.

Recognizing the crucial impacts of dispersal and noise intensity in ecosystems, this article explores a two-species stochastic competitive model with a Holling Type-II functional response, in which the intrinsic growth rates are driven by the Ornstein–Uhlenbeck process. Firstly, we demonstrate the existence and uniqueness of the global solution to the model, as well as confirming the boundedness of the moment. Secondly, we proceed to derive sufficient conditions to guarantee the asymptotic stability of the model’s positive equilibrium point and acquire the value of constant b that will affect this property. This indicates that the weaker the noise intensity, the closer the stochastic model approaches the positive equilibrium of the corresponding deterministic model in the mean sense. Furthermore, we build the model by introducing a proper Lyapunov function and provide sufficient conditions under which a stationary distribution exists. Finally, through several numerical simulations, we yield results indicating that weaker noise can ensure the existence and uniqueness of a stationary distribution. Furthermore, this article extends the existing ones.

In the present paper we study the existence and stability problems of positive periodic solutions to a Gilpin–Ayala competitive model with periodic coefficients on time scales. Firstly, based on Schauder’s fixed theorem, some sufficient conditions for the existence of positive periodic solution to the considered system are obtained. Furthermore, we establish asymptotic behavior by using the existence of periodic solutions. Since the considered system is based on an arbitrary time scale, our results are applicable to both discrete and continuous scenarios. We provide a specific example to verify the above results.

In an ecosystem, besides the basic relationships among populations within a community, many environmental factors may affect species growth. Accordingly, on the basis of predation fear and prey refuge, a stochastic competition model with impulsive effects is formulated and studied in this paper. First, by constructing the appropriate Lyapunov function, the existences of a unique global positive solution for the stochastic system is demonstrated. Then, using Itô formula, the stochastic Lyapunov function and some important inequalities, the sufficient conditions of extinction, non-mean persistence, mean persistence, random persistence and global attraction of the system are established. Finally, numerical simulations are implemented to comprehend the obtained results and illustrate the pivotal influence of the cost of fear, the strength of prey refuge, the environmental noise and the pulse interference on the predator population.

Under current competitive liner shipping market, it is crucial to explore the optimal shipping strategy for the subsistence and development of liner companies. In order to establish a liner shipping competitive model, we choose service quality, which can be measured by a range of unstructured data of relative items (such as delivery service, security, processing speed, user-friendliness) with big data analytics, as a key factor in the utility function and analyze the impact of service quality on the pricing strategy for container liner shipping context. By using the analytic hierarchy process, fuzzy comprehensive evaluation and time series forecasting method, the concrete data from South America container liner shipping market is analyzed via empirical study. The finding has demonstrated the model could yield management value for liner companies, and could provide theoretical guidance to formulate the optimal liner shipping strategy.

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion . Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia -carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.