Sustainable strategies for harvesting predators and prey in a fluctuating environment

Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response

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.

Dynamic analysis of a modified algae and fish model with aggregation and Allee effect

In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its main purpose was to further ascertain the dynamic relationship between algae and fish. Several critical conditions were investigated to guarantee the existence and stabilization of all possible equilibrium points, and ensure that the model could undergo transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and B-T bifurcation. Numerical simulation results of related bifurcation dynamics were provided to verify the feasibility of theoretical derivation, and visually demonstrate the changing trend of the dynamic relationship. Our results generalized and improved some known results, and showed that the aggregation and Allee effect played a vital role in the dynamic relationship between algae and fish.

Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect

In this paper, in order to explore the inhibition mechanism of algicidal bacteria on algae, we constructed an aquatic amensalism model with non-selective harvesting and Allee effect. Mathematical works mainly gave some critical conditions to guarantee the existence and stability of equilibrium points, and derived some threshold conditions for saddle-node bifurcation and transcritical bifurcation. Numerical simulation works mainly revealed that non-selective harvesting played an important role in amensalism dynamic relationship. Meanwhile, we proposed some biological explanations for transcritical bifurcation and saddle-node bifurcation from the aspect of algicidal bacteria controlling algae. Finally, all these results were expected to be useful in studying dynamical behaviors of aquatic amensalism ecosystems and biological algae controlling technology.