Department of Mathematics, National Institute of Technology Raipur, Raipur, CG, 492010, India.
Acta Biotheor. 2022 Feb 4;70(1):11. doi: 10.1007/s10441-022-09435-5.
Predation and escaping from predation through hiding are two fundamental phenomena in ecology. The most common approach to reducing the chance of predation is to use a refuge. Here, we consider a three species fishery model system with prey refuge induced by a Holling type-II functional response. These three species of fish populations are named prey, middle predator, and top predator. Harvesting is employed in most fishery models to achieve both ecological and commercial benefits. Research proves that non-linear harvesting (Michaelis-Menten type) returns more realistic outcomes. So, we have combined the Michaelis-Menten type of harvesting efforts for all populations. Uniform boundedness conditions for the solutions of the model are discussed. The existence conditions for possible equilibrium points with stability are presented. We explain the dynamical behavior at each equilibrium point through bifurcation analysis. The persistent criteria of the system are examined. Bionomic equilibrium and optimal harvesting control using Pontryagin's maximum principle are calculated. For validation of the model in the real world, we have implemented this in the freshwater ecosystem of Lake Victoria. Extraction of native fish species and ecological balances are the foremost solicitude of Lake Victoria. We may resolve this concern partially by implementing prey refuge, since it may sustain the ecology of Lake Victoria, and therefore also its economical importance. Lake Victoria is acclaimed worldwide for the trade of fishing. Also, it provides the largest employment in east-central Africa and is beneficial to fishing equipment manufacturers. So, the bionomic equilibrium and harvesting control have significant applications in the fisheries. All the analytical studies are verified by numerical simulations. We have plotted phase portraits, bifurcation diagrams, Lyapunov exponents to explore the dynamics of the proposed model.
捕食和逃避捕食是生态学中的两个基本现象。减少被捕食的最常见方法是使用避难所。在这里，我们考虑了一个具有 II 型 Holling 功能反应诱导的猎物避难所的三种鱼类渔业模型系统。这三种鱼类种群分别命名为猎物、中间捕食者和顶级捕食者。收获是大多数渔业模型中用来实现生态和商业利益的方法。研究证明，非线性收获（米氏类型）会产生更现实的结果。因此，我们对所有种群的收获努力都采用了米氏类型。讨论了模型解的一致有界性条件。提出了存在平衡点及其稳定性的条件。我们通过分岔分析解释了每个平衡点的动态行为。检查了系统的持续存在条件。利用庞特里亚金极大值原理计算了生物平衡和最优捕捞控制。为了在现实世界中验证模型，我们在维多利亚湖的淡水生态系统中实现了这一点。提取本地鱼类物种和生态平衡是维多利亚湖最关心的问题。通过实施猎物避难所，我们可以部分解决这个问题，因为它可以维持维多利亚湖的生态系统，因此也可以维持其经济重要性。维多利亚湖因其渔业贸易而闻名于世。它还为中东部非洲提供了最大的就业机会，并有利于渔具制造商。因此，生物平衡和捕捞控制在渔业中有重要的应用。所有的分析研究都通过数值模拟进行了验证。我们绘制了相图、分岔图和李雅普诺夫指数，以探索所提出模型的动力学。
