Qualitative analysis and simulations of a ratio-dependent May-Holling-Tanner predator-prey model with an alternative food source for the predator

Abstract

In this work, a May-Holling-Tanner ratio-dependent predator-prey model is studied with an alternative food source for the predator, described by a two-dimensional system of ordinary differential equations. We study the existence and uniqueness of the solutions of the mentioned above system. In addition, the boundedness and positivity of these solutions are analyzed and we establish conditions for the local stability of a simplified model, through a differentiable equivalence. Likewise, the Python programming language is used to perform the simulations using the Runge-Kutta numerical method of order four with the aim of showing the different cases of qualitative analysis.

Keywords

• may-holling-tanner model
• ratio-dependent
• alternative food
• simulations