Abstract

In this paper, considering the aggregation effect and Allee effect of cyanobacteria population and the harvesting of both cyanobacteria and fish by human beings, we put forward a new cyanobacteria-fish model with two harvesting terms and a modified Holling type IV functional response function. The main purpose of this paper is to further understand the influence of harvesting terms on the dynamic behavior of 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. From the perspective of biology, we conclude that the harvesting terms can determine the survival mode of cyanobacteria and fish. Finally, concrete examples of our model are given through numerical simulation to verify and enrich the theoretical results.