Analysis of open-water plankton-fish-mussel system under the influence of environmental noises

Abstract

In this article, we consider a mathematical model consisting of fish and mussel population in presence of plankton as common food source in marine ecosystem. The model is constructed considering all possible biological relationships among plankton (nutrient), fish and mussel. Non constant death rate is introduced for mussel population. To avoid ignoring any environmental factors, we consider some important parameters as stochastic. Existence and uniqueness of global positive solutions, boundedness of solutions are proved mathematically. Conditions for extinction of fish and mussel population are derived at. From these conditions, we have reached at some conclusion which are verified numerically. We have established the conditions for which the model is persistent in mean. We have proved that the solutions are globally attractive in mean. Numerical simulations are performed by using MATLAB to justify the mathematical findings. Numerically, we have investigated several useful facts and have achieved some conclusions. For extension of this study, a model is proposed at the end.