Open AccessLotka-Volterra Model of Wastewater Treatment in Bioreactor System using 4th Order Runge-Kutta Method
Author(s) -
Zaileha Md Ali,
Ezmir Faiz Mohd Puard,
Muhamad Hariz Sudin,
Nur Aziean Mohd Idris
Publication year - 2022
Publication title -
science letters
Language(s) - English
Resource type - Journals
eISSN - 2682-8626
pISSN - 1675-7785
DOI - 10.24191/sl.v16i1.15284
Subject(s) - ordinary differential equation , substrate (aquarium) , differential equation , mathematics , runge–kutta methods , nonlinear system , equilibrium point , wastewater , predation , biological system , control theory (sociology) , environmental science , mathematical analysis , environmental engineering , ecology , computer science , physics , biology , quantum mechanics , control (management) , artificial intelligence
Wastewater treatment is essential to preserve the ecosystem and to ensure water resources are uncontaminated. This paper presents the Lotka-Volterra model of nonlinear ordinary differential equations of the interaction between predator-prey and substrate. The dimensionless ordinary differential equations of the model are solved using the 4th Order Runge-Kutta method (RK4) in MATLAB®. This study discusses the behaviour parameters of predators, prey and substrate. The results are shown graphically for different values of each parameter. Hence, the biological reaction of clean water from the interaction of predator-prey and substrate in wastewater treatment is identified. The higher the concentration of prey, the faster the concentration of substrate reaches 0 with and without the natural death of prey. The clean water will be produced whenever the concentration of prey and the concentration of predator are in balance regardless of the natural death rate. Stability analysis using the Jacobian matrix at the equilibrium point is also performed to determine the stability of the system.