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In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following rational difference equationwhere the inital values x −1 and x 0 and α, β and γ with γ = 0 are nonnegative real numbers. Its solutions are associated with generalized Tribonacci numbers.

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In this paper, we study the boundedness, persistence, and periodicity of the positive solutions and the global asymptotic stability of the positive equilibrium points of the system of difference equationswhere A ∈ (0, ∞) and the initial conditions x i , y i , z i ∈ (0, ∞), i = -1, 0. MSC: 39A10; 39A30

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).