On the dynamical behaviors of a quadratic difference equation of order three

Abstract

In this paper provides proof of the existence of periodicity, asymptotic behavior, and boundedness of the following quadratic three order difference equation, n = 0, 1, 2, . . . , constants ζ, η, ρ, κ, α, β and γ are positive real numbers and the initial conditions w −2 , w −1 and w 0 are arbitrary non zero real numbers.