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Vol.11, No.4, November 2022. ISSN: 2217-8309 eISSN: 2217-8333
TEM Journal
TECHNOLOGY, EDUCATION, MANAGEMENT, INFORMATICS Association for Information Communication Technology Education and Science |
Global Stability Analysis of a Certain Second-Order Rational Difference Equation with Nonlinear Terms
Midhat Mehuljić, Vahidin Hadžiabdić, Jasmin Bektešević, Adnan Mašić, Fatih Destović
© 2022 Fatih Destović, 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 4, Pages 1924-1929, ISSN 2217-8309, DOI: 10.18421/TEM114-61, November 2022.
Received: 09 September 2022. Revised: 19 October 2022.
Abstract:
In this paper we observed the global dynamics and the occurrence of a certain bifurcation for the corresponding values of a certain rational difference equation of the second order with analyzed quadratic terms. The analysis of the local stability of the unique equilibrium point, as well as the unique periodic solution of period two, was performed in detail. The constraint of the equations on both sides for the corresponding values of the parameters is proved and on this basis the global stability is analyzed. The existence of Neimark-Sacker bifurcation with respect to the arrangement of equilibrium points has been proven. Thus, the basins of attraction have been determined in full for all the positive values of the parameters and all the positive initial conditions.
Keywords – – basins of attraction, difference equation, equilibrium, stability, period two solution. |
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