Convergence, Periodicity and Bifurcations for the Two-parameter Absolute-Difference Equation.

Authors :: Kent, C. M.
Sedaghat, H.
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]

Subjects :: DIFFERENTIAL equations
CALCULUS
REAL numbers
MATHEMATICS
STOCHASTIC convergence
MATHEMATICAL functions

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