Multistability Analysis of a Mathematical Model of the Interaction of Opuntia stricta and Dactylopius opuntia

Abstract

We develop a Mathematical model showing the main dynamical regimes of the weed Opuntia stricta and the insect, Dactylopius opuntiae interaction. We prove that under appropriate conditions a positive solution of the system is asymptotically stable, unstable or it is a periodic solution. Stable equilibria points are characterised by endemic and epidemic populations. Endemic populations are regulated by the number of cacti trees available. Epidemic populations are limited by the total number of trees because mass attack of the insects may overcome resistance of any tree. Mathematics Subject Classification: 93A30, 92B05, 34C23 Keywords: Dynamical regimes, asymptotic behaviour of solutions, bifurcation properties of solutions