Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.