Global Stability Analysis of a Certain Second-Order Rational Difference Equation with Nonlinear Terms
Global Stability Analysis of a Certain Second-Order Rational Difference Equation with Nonlinear Terms
Author(s): Midhat Mehuljić, Vahidin Hadžiabdić, Jasmin Bektešević, Adnan Mašić, Fatih DestovićSubject(s): ICT Information and Communications Technologies
Published by: UIKTEN - Association for Information Communication Technology Education and Science
Keywords: basins of attraction; difference equation; equilibrium; stability; period two solution
Summary/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.
Journal: TEM Journal
- Issue Year: 11/2022
- Issue No: 4
- Page Range: 1924-1929
- Page Count: 6
- Language: English
