On a recursive sequence
Purpose - The aim in this paper is to investigate the dynamics of difference equation y(n+1) = (py(n) + y(n-k))/(qy(n) + y(n-k)) n = 0, 1, 2.... where k is an element of {1, 2, 3,...}, the initial conditions y(-k),... y(-1), y(0) and the parameters p and q are non-negative. Design/methodology/approach - The paper studies characteristics such as the character of semicycles, periodicity and the global stability of the above mentioned difference equation. Findings - In particular, the results solve the open problem introduced by Kulenovic and Ladas in their monograph, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Originality/value - The global behaviour of the solutions of equation y(n+1) = (py(n) +Yn-k)/(qy(n)+ y(n-k)), n=0,1,2.... were investigated providing valuable conclusions on practical data.
difference equations cybernetics