<p>In this paper, we employed the mathematical model to show the aggregation effect of algal blooms to explore the relationship between cyanobacteria blooms and filter-feeding fish. The existence of equilibrium points and the conditions for the stability of equilibrium points have been derived. A proposed mathematical model is used to investigate transcritical bifurcation, Hopf bifurcation and direction of Hopf bifurcation. The stability of the limit cycle occurring through Hopf-bifurcation is carried out. Bifurcation analysis supports the theoretical explanation. We observed that if the cyanobacteria aggregation area increased over a certain threshold, filter-feeding fish would become extinct. Cyanobacteria aggregation can influence the eating habits of filter-feeding fish and protect them from predators. Numerical simulations show that the aggregation effect of cyanobacteria plays a significant role in the dynamic connection. A weakly nonlinear analysis has been carried out to determine the magnitude of the Turing instability. Furthermore, we explored the Turing Insatiability condition for spatial patterns resulting from spatial systems and evaluated the pattern formation over time. Our analytical findings were corroborated by numerical solutions, which showed that the coexistence of all population classes is dependent on diffusion.</p>