The global asymptotic stability of a system of difference equations

摘要

This paper deals with the global asymptotic stability of the unique positive equilibrium point and the rate of convergence of positive solutions of the system of two recursive sequences, x_(n+1) = A +(yn?m/yn), y_(n+1) = A + (x_(n?m)/x_n), n = 0, 1, . . ., and m ∈ Z~+, where A ∈ (0,∞) x_(-i) and y_(-i) are arbitrary positive numbers for i = 0, 1, . . . ,m. Also, we present some results about the general behaviour of solutions of aforementioned system. Finally, some numerical examples are given to demonstrate the effectiveness of the results obtained.