On the global attractivity and oscillations in a class of second order difference equations from macroeconomics

Details On the global attractivity and oscillations in a class of second order difference equations from macroeconomics On the global attractivity and oscillations in a class of second order difference equations from macroeconomics

2010-02-16

arxiv.org/abs/1002.3090v1

Mathematics

Dynamical Systems

the final version of this paper will be published in Journal of Difference Equations and Applications

Scientific paper

New global attractivity criteria are obtained for the second order difference equation \[ x_{n+1}=cx_{n}+f(x_{n}-x_{n-1}),\quad n=1, 2, ... \] via a Lyapunov-like method. Some of these results are sharp and support recent related conjectures. Also, a necessary and sufficient condition for the oscillation of this equation is obtained using comparison with a second order linear difference equation with positive coefficients.

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