Abstract—In this paper a nonlinear mathematical model is proposed to analyze the effect of decreasing level of dissolved oxygen on the survival of aquatic species in the water body in the presence of nutrients. This model has four nonlinear differential equations consisting of four state variables accounting for concentration of nutrients, density of algae, density of fish population, and concentration of dissolved oxygen. The three equilibrium points have been obtained to understand the dynamic behavior of the system. The conditions for existence of these equilibrium points are obtained. The stability analysis is conducted on each equilibrium point by considering variational matrix and using Routh-Hurwitz criteria. The nonlinear stability behavior of an equilibrium point considered to be critical is analyzed by applying Liapunov’s direct method.

Index Terms—Algae, dissolved oxygen, Liapunov’s function, mathematical model, nutrients.

Shikha Chaturvedi is with Fr. C. Rodrigues Institute of Technology, Vashi, Maharashtra, India. She is also with Shri J.J.T. University, Jhunjhunu, Rajasthan, India (email: cshikha11@gmail.com).
Prabha S. Rastogi is with Shri J.J.T. University, Jhunjhunu, Rajasthan, India.

Cite: Shikha Chaturvedi, Prabha S. Rastogi, "Modeling the Effect of Decreasing Dissolved Oxygen on Fish Population Survival in Aquatic Body in the Presence of Nutrients," International Journal of Applied Physics and Mathematics vol. 6, no. 1, pp. 9-16, 2016.