Department of Mathematics, Periyar University, Salem, India.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, India.
J Biol Dyn. 2023 Dec;17(1):2164803. doi: 10.1080/17513758.2022.2164803.
In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented.
本文提出并研究了一个具有疾病的新型随机四物种捕食者-被捕食者模型。首先，我们根据一些生物学假设给出了随机模型，并建立了全局正解的存在性。此外，还给出了物种永久灭绝的条件。上述性质有助于拯救生态系统中处于危险中的种群。通过李雅普诺夫函数，我们讨论了我们模型的正平衡点的渐近稳定性。此外，还表明系统具有平稳分布，并指出了稳定生物群落的存在。最后，我们提出的模型的结果揭示了在捕食者种群中添加替代食物源时随机波动对四物种生态系统的影响。为了说明我们的理论发现，给出了一些数值模拟。
