Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation
Joint Authors
Kulenovic, Mustafa R. S.
Nurkanović, Z.
Moranjkić, S.
Nurkanović, M.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-08
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
We investigate the global asymptotic stability of the following second order rational difference equation of the form xn+1=Bxnxn-1+F/bxnxn-1+cxn-12, n=0,1,…, where the parameters B, F, b, and c and initial conditions x-1 and x0 are positive real numbers.
The map associated with this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space.
In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.
Also, we show that considered equation exhibits the Naimark-Sacker bifurcation resulting in the existence of the locally stable periodic solution of unknown period.
American Psychological Association (APA)
Kulenovic, Mustafa R. S.& Moranjkić, S.& Nurkanović, M.& Nurkanović, Z.. 2018. Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation. Discrete Dynamics in Nature and Society،Vol. 2018, no. 2018, pp.1-22.
https://search.emarefa.net/detail/BIM-1152759
Modern Language Association (MLA)
Kulenovic, Mustafa R. S.…[et al.]. Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation. Discrete Dynamics in Nature and Society No. 2018 (2018), pp.1-22.
https://search.emarefa.net/detail/BIM-1152759
American Medical Association (AMA)
Kulenovic, Mustafa R. S.& Moranjkić, S.& Nurkanović, M.& Nurkanović, Z.. Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation. Discrete Dynamics in Nature and Society. 2018. Vol. 2018, no. 2018, pp.1-22.
https://search.emarefa.net/detail/BIM-1152759
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152759