Dynamics of a discrete Lotka-Volterra model

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 = alpha X-n - beta XnYn/1 + gamma X-n, y(n+1) = delta y(n) + epsilon X(n)y(n)/1 + eta y(n), where parameters alpha, beta, gamma, delta, epsilon, eta is an element of R+, and initial conditions x(0), y(0) 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.