Lotka-volterra model of wastewater treatment in bioreactor system using 4th order runge-kutta method / Zaileha Md Ali ...[et al.]

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.