On Stability Analysis of Higher-Order Rational Difference Equation - Abdul Khaliq; H. S. Alayachi; M. S. M. Noorani; A. Q. Khan (Discrete Dynamics in Nature and Society)
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results.