Stabilizing a mathematical model of plant species interaction

Abstract

In this paper, we will consider how to stabilize a mathematical model of plant species interaction which is modelled by using Lotka-Volterra system. We first identify the unstable steady states of the system, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. We further stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas.