Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation
| Autor: | Senada Kalabušić, M. R. S. Kulenović, M. Mehuljić |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2014 (2014) |
| Druh dokumentu: | article |
| ISSN: | 1026-0226 1607-887X 52441482 |
| DOI: | 10.1155/2014/920410 |
| Popis: | We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1>0, for all n≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β=B=0, in which case we show that such equation exhibits a global period doubling bifurcation. |
| Databáze: | Directory of Open Access Journals |
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