Dynamics of a discrete lotka-volterra model

Abstract

In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by xn+1 = αxn - βxnyn/1 + γxn, yn+1 = δyn + εxnyn/1 + ηyn, where parameters a,β, γ , δ, ε,η ε ℝ+, and initial conditions x0, y0 are positive real numbers. Moreover, the rate of convergence of a solution that converges to the unique positive equilibrium point is discussed. Some numerical examples are given to verify our theoretical results. © 2013 Din; licensee Springer.