Stability Analysis of a System of Exponential Difference Equations

We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: x(n+1) = (alpha(1) + beta(1)e(-xn) + + gamma(1)e(-xn-1))/(a(1) + b(1)y(n) + c(1)y(n-1)), y(n+1) = (alpha(2) + beta(2)e(-yn) + gamma 2e(-yn-1))/(a(2) + b(2)x(n) + c(2)x(n-1)), where the parameters alpha(i), beta(i), gamma(i), a(i), b(i), and c(i) for i epsilon {1, 2} and initial conditions x(0), x(-1), y(0), and y(-1) are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results.