Locally stability analysis of the Phytoplankton-Nitrogen- Phosphate-Sediment dynamical system: A study case at Karimunjawa aquaculture system, Central Java

Abstract

Disturbance of water environment due to organic enrichment by fish activities may result in the reduction of water quality and sediments. The relative importance of N and P limitation and released from organic sediment is still an open question. The aim of this paper is to analyze the locally asymptotic stable from a dynamical system model in the equilibrium of water ecosystem. Mathematical models are resultant of interaction among four main variables. i.e.nitrogen and phosphate concentration, phytoplankton abundance, and sediment in the water ecosystem at Menjangan Besar, Karimunjawa islands. The four variables are non-linear system differential equation that will form the dynamical system mathematical model. Local stability was determined by using Taylor series and Jacobian matrix. The system will be locally asymptotically stable if eigenvalues are negative. Numerical simulation was used to analyze the dynamic behavior of the system. From numerical simulation results base, it is concluded that equilibrium points. Because all eigenvalues of the Jacobian matrix ware negative, the dynamic system model was locally asymptotically stable.