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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− p(α + (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, andw0 are positive real numbers. Some numerical examples are given to verify our theoretical results.

On Stability Analysis of Higher-Order Rational Difference Equation