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

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 asympt...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-12, Vol.1397 (1), p.12066
Main Authors: Triyana, E, Widowati, Putro, S P
Format: Article
Language:English
Subjects:
Aquaculture
Asymptotic properties
Differential equations
Dynamic stability
Dynamical systems
Eigenvalues
Environment models
Jacobi matrix method
Jacobian matrix
Mathematical models
Nitrogen
Physics
Phytoplankton
Plankton
Sediments
Stability analysis
Taylor series
Water quality
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1397/1/012066