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We investigate the local and global character of the equilibrium and the local stability of the period-two solution of the difference equation x n+1 = βx n x n-1 +γ x 2 n-1 +δx n Bx n x n-1 +Cx 2 n-1 +Dx n where the parameters β, γ , δ, B, C, D are nonnegative numbers which satisfy B + C + D > 0 and the initial conditions x -1 and x 0 are arbitrary nonnegative numbers such that Bx n x n-1 + Cx 2 n-1 + Dx n > 0 for all n ≥ 0. MSC: Primary 39A10; 39A11; secondary 39A30doi:10.1186/1687-1847-2014-68 fatcat:ewr5c6nnybdwtaieytjmqcj7ji