Mathematical analysis of a food chain: prey - predator - biological - control

Abstract

In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.

Keywords

• Predator - Prey
• Food Chain
• Biological Control
• Scenarios Extinction
• Asymptotic Stability
• Runge - Kutta