Global behavior of a second order difference equation with two-period coefficient
Abstract
In this paper, we present a detailed study of the following difference equation
x_{n+1}=((α_{n})/(1+x_{n}x_{n-1})), n∈ℕ₀,
where the sequence (α_{n})_{n≥0} is positive, real, periodic with period two and the initial values x₋₁, x₀ are nonnegative real numbers. By this study, we determine global behavior of positive solutions of the above mentioned equation. We also give closed forms of its general solution.
x_{n+1}=((α_{n})/(1+x_{n}x_{n-1})), n∈ℕ₀,
where the sequence (α_{n})_{n≥0} is positive, real, periodic with period two and the initial values x₋₁, x₀ are nonnegative real numbers. By this study, we determine global behavior of positive solutions of the above mentioned equation. We also give closed forms of its general solution.
Keywords
Closed form solution; difference equations; global behavior; periodic solution; periodic coefficients.
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