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Convergence, Periodicity and Bifurcations for the Two-parameter Absolute-Difference Equation.
- Source :
- Journal of Difference Equations & Applications; Aug2004, Vol. 10 Issue 9, p817-841, 25p
- Publication Year :
- 2004
-
Abstract
- The two-parameter absolute difference equation x<subscript>n+1</subscript> = ∣ax<subscript>n</subscript>-bx<subscript>n-1</subscript>∣ is studied. Based on the parameter values a, b and a pair of initial values, we consider the existence and bifurcations of solutions having one or more of the following properties: (i) unbounded, (ii) convergent (to zero or to a positive constant) (iii) monotonic, (iv) periodic and (v) non-periodic oscillatory. The semiconjugate first order equation satisfied by the ratios (x<subscript>n</subscript>/x<subscript>n-1</subscript> is used to significant advantage for points (a, b) in certain regions of the parameter plane. Some open problems and conjectures are presented. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 10
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 14399310
- Full Text :
- https://doi.org/10.1080/10236190410001685049