Stability analysis of solutions of certain May's host-parasitoid model by using KAM theory

Abstract

We use the Kolmogorov-Arnold-Moser (KAM) theory to investigate the stability of solutions of a system of difference equations, a certain class of a generalized May's host-parasitoid model. We show the existence of the extinction, interior, and boundary equilibrium points and examine their stability. When the rate of increase of hosts is less than one, the zero equilibrium is globally asymptotically stable, which means that both populations are extinct. We thoroughly describe the dynamics of 1:1 non-isolated resonance fixed points and have used the KAM theory to determine the stability of interior equilibrium point. Also, we have conducted several numerical simulations to support our findings by using the software package Mathematica.

Keywords

• difference equations
• fixed point
• area-preserving map
• kam theory