Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

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 fo...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2014-01, Vol.2014 (2014), p.718-730-266
Main Authors: Kalabusic, Senada, Kulenovic, M.R.S, Mehuljic, M
Format: Article
Language:English
Subjects:
Asymptotic properties
Bifurcation theory
Bifurcations
Colleges & universities
Difference equations
Dynamics
Economic models
Equations, Quadratic
Equilibrium
Initial conditions
Mathematical analysis
Mathematical research
Mathematics
Period doubling
Stability
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2014/920410