Vol.11, No.2, May 2022.                                                                                                                                                                                   ISSN: 2217-8309

                                                                                                                                                                                                                        eISSN: 2217-8333


TEM Journal



Association for Information Communication Technology Education and Science

Existence and Local Stability of Prime Period-two Solutions of Certain Quadratic Rational Second Order Difference Equation


Midhat Mehuljić, Vahidin Hadžiabdić, Jasmin Bektešević


© 2022 Vahidin Hadžiabdić, published by UIKTEN. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. (CC BY-NC-ND 4.0)


Citation Information: TEM Journal. Volume 11, Issue 2, Pages 914-919, ISSN 2217-8309, DOI: 10.18421/TEM112-53, May 2022.


Received: 04 March 2022.

Revised:   24 April 2022.
Accepted: 03 May 2022.
Published: 27 May 2022.




In this paper we proved the existence and local stability of prime period-two solutions for the equation 𝐱𝐧􀬾𝟏 􀵌 𝛂𝐱𝐧 𝟐 􀬾𝛃𝐱𝐧􀬾𝛄𝐱𝐧􀰷𝟏 𝐀𝐱𝐧 𝟐 􀬾𝐁𝐱𝐧􀬾𝐂𝐱𝐧􀰷𝟏 , for certain values of parameters ,,,A,B,C0, 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.


Keywords –bifurcation, difference equation, equilibrium, local stability, prime period-two.



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