Document Type

Article

Date of Original Version

4-27-2014

DOI

10.1155/2014/920410

Abstract

We investigate the local stability and the global asymptotic stability of the difference equation � �+1 = (�� 2 � + �� � � �−1 + �� �−1 ) / (�� 2 � + �� � � �−1 + �� �−1 ), � = 0, 1, . . . with nonnegative parameters and initial conditions such that �� 2 � + �� � � �−1 + �� �−1 > 0, for all � ≥ 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 � = � = 0, in which case we show that such equation exhibits a global period doubling bifurcation.

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Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

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