Key Laboratory for Subtropical Oceans & Lakes Environment and Biological Resource Utilization Technology of Zhejiang, Wenzhou University, Wenzhou 325035, China.
School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China.
Math Biosci Eng. 2023 May 26;20(7):12599-12624. doi: 10.3934/mbe.2023561.
In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results.
本文考虑了蓝藻种群的聚集效应和 Allee 效应，以及人类对蓝藻和鱼类的捕捞，提出了一个具有两个捕捞项和修正 Holling Ⅳ型功能反应函数的蓝藻-鱼类新模型。本文的主要目的是进一步阐明捕捞项对蓝藻-鱼类模型动态行为的影响。给出了几个内平衡点存在和稳定性的临界条件。还研究了经济平衡点和最大可持续总产量问题。模型表现出几种分岔，如跨临界分岔、鞍结分岔、Hopf 分岔和 Bogdanov-Takens 分岔。从生物学的角度得出结论，蓝藻和鱼类的生存模式可以由捕捞项来决定。最后，通过数值模拟给出了我们模型的具体实例，以验证和丰富理论结果。
