Dynamical analysis of toxin-producing Microcystis aeruginosa aggregation on filter-feeding fish in aquatic ecosystem

The predator-prey interaction in mathematical ecology is a basic phenomenon in nature that has an important impact on community organization and on preserving the ecological diversity. In this research work, we have developed an unique aquatic ecological model to investigate the interaction between Microcystis aeruginosa and filter-feeding fish in presence of toxicity. This model specifically focuses on describing the phenomenon of Microcystis aeruginosa aggregation and the effect of toxin producing Microcystis aeruginosa blooms on filter-feeding fishes. Holling type II and Holling type III functional responses are used in our proposed model. Here, we have analyzed the model parameters to examine the stability of all equilibrium points in our system. Our system shows local bifurcations, including transcritical, saddle-node, Hopf, generalized Hopf, Cusp bifurcation and Bogdanov-Takens. Further, we have seen global bifurcation, particularly homoclinic bifurcation. Additionally, we have provided evidence of the hysteresis phenomena and basins of attraction to support the existence of bi-stability. Multiple numerical examples support each of these theoretical findings.