Dynamic analysis of a new aquatic ecological model based on physical and ecological integrated control

Abstract

Within the framework of physical and ecological integrated control of cyanobacteria bloom, because the outbreak of cyanobacteria bloom can form cyanobacteria clustering phenomenon, so a new aquatic ecological model with clustering behavior is proposed to describe the dynamic relationship between cyanobacteria and potential grazers. The biggest advantage of the model is that it depicts physical spraying treatment technology into the existence pattern of cyanobacteria, then integrates the physical and ecological integrated control with the aggregation of cyanobacteria. Mathematical theory works mainly investigate some key threshold conditions to induce Transcritical bifurcation and Hopf bifurcation of the model (2.1), which can force cyanobacteria and potential grazers to form steady-state coexistence mode and periodic oscillation coexistence mode respectively. Numerical simulation works not only explore the influence of clustering on the dynamic relationship between cyanobacteria and potential grazers, but also dynamically show the evolution process of Transcritical bifurcation and Hopf bifurcation, which can be clearly seen that the density of cyanobacteria decreases gradually with the evolution of bifurcation dynamics. Furthermore, it should be worth explaining that the most important role of physical spraying treatment technology can break up clumps of cyanobacteria in the process of controlling cyanobacteria bloom, but cannot change the dynamic essential characteristics of cyanobacteria and potential grazers represented by the model (2.1), this result implies that the physical spraying treatment technology cannot fundamentally eliminate cyanobacteria bloom. In a word, it is hoped that the results of this paper can provide some theoretical support for the physical and ecological integrated control of cyanobacteria bloom.

Keywords

• cyanobacteria bloom
• potential grazers
• aggregation
• hopf bifurcation
• transcritical bifurcation