STABILITY ANALYSIS OF ECOLOGICAL MATHEMATICAL MODEL OF OXYGEN–PHYTOPLANKTON–ZOOPLANKTON

Abstract

Aquatic ecosystems are strongly influenced by interactions among dissolved oxygen concentration, phytoplankton, and zooplankton populations. Phytoplankton play a fundamental role as primary producers through photosynthesis, while zooplankton act as consumers regulating phytoplankton growth. In this study, a mathematical model describing the interaction between oxygen concentration, phytoplankton, and zooplankton is developed and analyzed. The model is formulated as a system of nonlinear ordinary differential equations. Analytical investigations include the positivity and boundedness of solutions, equilibrium analysis, and local stability analysis using the Jacobian matrix and the Routh–Hurwitz stability criterion. Several equilibrium points are obtained, including the trivial equilibrium, boundary equilibria, and an interior equilibrium representing coexistence among the three ecological components. Numerical simulations are performed using MATLAB to illustrate the dynamical behavior of the system. The results indicate that the stability of the system depends on ecological parameters such as phytoplankton growth rate, zooplankton mortality, and oxygen production. The analytical and numerical results demonstrate that the ecosystem can reach stable states under certain parameter conditions.