Bifurcation analysis of a new aquatic ecological model with aggregation effect

Abstract

In the paper, to better understand the dynamic relationship between Microcystis aeruginosa and filter-feeding fish, we have constructed a new aquatic ecological model to describe the aggregation effect of Microcystis aeruginosa. Mathematical theory works mainly investigated the critical threshold condition through the discovery of transcritical bifurcation, saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. The numerical simulation works mainly revealed that Microcystis aeruginosa aggregation effect has played an important role in the dynamic relationship with the aid of bifurcation analysis, which also in turn proved the validity of theoretical derivation. The results showed that if the Microcystis aeruginosa aggregation area became larger and larger, and exceeded a critical threshold, the filter-feeding fish would eventually go extinct. Furthermore, it should be stressed that Microcystis aeruginosa aggregation can effectively control the feeding dynamic behavior of filter-feeding fish and provide shelter from predators. Finally, all these results were expected to be useful in studying population dynamics of some aquatic ecosystems.