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27. 5. 2022.
Existence and Local Stability of Prime Period-two Solutions of Certain Quadratic Rational Second Order Difference Equation
In this paper we proved the existence and local stability of prime period-two solutions for the equation 𝐱𝐧𝟏 𝛂𝐱𝐧 𝟐 𝛃𝐱𝐧𝛄𝐱𝐧𝟏 𝐀𝐱𝐧 𝟐 𝐁𝐱𝐧𝐂𝐱𝐧𝟏 , for certain values of parameters ,,,A,B,C0, where ++>0 , A+B+C>0, and where the initial conditions x₋₁, x₀>0 are arbitrary real numbers such that at least one is strictly positive. For the obtained periodic solutions, it is possible to be locally asymptotically stable, saddle points or nonhyperbolic points. The existence of repeller points is not possible.