School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
College of Science, Guilin University of Technology, Guilin 541004, China.
Math Biosci Eng. 2023 Jan;20(2):3700-3720. doi: 10.3934/mbe.2023173. Epub 2022 Dec 9.
In the predator-prey system, predators can affect the prey population by direct killing and inducing predation fear, which ultimately force preys to adopt some anti-predator strategies. Therefore, it proposes a predator-prey model with anti-predation sensitivity induced by fear and Holling-Ⅱ functional response in the present paper. Through investigating the system dynamics of the model, we are interested in finding how the refuge and additional food supplement impact the system stability. With the changes of the anti-predation sensitivity (the refuge and additional food), the main result shows that the stability of the system will change accordingly, and it has accompanied with periodic fluctuations. Intuitively the bubble, bistability phenomena and bifurcations are found through numerical simulations. The bifurcation thresholds of crucial parameters are also established by the Matcont software. Finally, we analyze the positive and negative impacts of these control strategies on the system stability and give some suggestions to the maintaining of ecological balance, we perform extensive numerical simulations to illustrate our analytical findings.
在捕食者-猎物系统中，捕食者可以通过直接捕杀和引发捕食恐惧来影响猎物种群，这最终迫使猎物采取一些反捕食策略。因此，本文提出了一个具有恐惧诱导的捕食敏感性和 Holling-Ⅱ功能反应的捕食者-猎物模型。通过研究模型的系统动态，我们感兴趣的是研究避难所和额外食物补充如何影响系统稳定性。随着反捕食敏感性（避难所和额外食物）的变化，主要结果表明系统的稳定性将相应地发生变化，并伴随着周期性波动。通过数值模拟直观地发现了气泡、双稳现象和分岔。使用 Matcont 软件确定了关键参数的分岔阈值。最后，我们分析了这些控制策略对系统稳定性的正反两方面影响，并对维持生态平衡提出了一些建议，我们进行了广泛的数值模拟来说明我们的分析结果。
