A mathematical model with a trophic chain predation based on the ODEs to describe fish and plankton dynamics

Abstract

The aim of this paper is the formulation and the study of a prey-predator model to describe fish and plankton population dynamics, with three developmental stages of the fish population (larva, juvenile and adult). First, we develop a mathematical model based on the ODEs, describing the dynamics of the various classes for the sh population depending on the plankton in a general framework. Then, we are interested in the model in the case of a trophic chain predation for the sh population. Finally, we continue our study through numerical simulations of the model in different fishing areas. The obtained numerical results confirm the mathematical analysis and allow us to have an idea on the development of the
fish population in a fishing area.