In this paper, we propose an adaptive mathematical model for the three species: nutrient, algae, and small fish predator-prey system. We formulate the model for the system, investigate sufficient conditions for the existence of positive periodic solutions, and checking the validity of the model. Then we study the stability, and asymptotical behaviours of the solutions with respect to the parameters.

food chain, predator-prey system, stability, Lotka-Volterra system, positive solution, equilibrium.