Stability analysis of a discrete ecological model

Abstract

In this paper, we study the qualitative behavior of following discrete-time population model: xn+1=a+bxn+rxn-1exp-y(n),yn-1=g+eyn+hyn-1exp-x(n), where parameters a, b, r, g, e, h and initial conditions x0, x-1, y0, y-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results.

Keywords

• population models
• difference equations
• steady-states
• boundedness
• local and global character