Stability Analysis of a System of Exponential Difference Equations

Abstract EN

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: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-yn-1)/(a2+b2xn+c2xn-1), where the parameters αi, βi, γi, ai, bi, and ci for i∈{1,2} and initial conditions x0, x-1, y0, 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.