Exponentially Asymptotically Constant Systems Of Difference Equations With An Application To Hyperbolic Equilibria
Journal Of Difference Equations And Applications
Mathematics and Computer Science
In a recent paper, Agarwal and Pituk have considered scalar linear difference equations whose coefficients are asymptotically constant and whose corresponding perturbations are exponentially small. Using the method of generating functions and results from complex analysis, they derived an asymptotic representation for solutions, which was then applied to study the asymptotic behaviour of solutions of certain nonlinear autonomous scalar difference equations near a hyperbolic equilibrium. Here, we first show using standard matrix analysis how their results can be extended to systems of linear difference equations and that the error estimates can be made more precise. Our method also can be extended to weakly nonlinear systems. That result can in turn be used to analyze solutions of some autonomous nonlinear difference systems near an equilibrium.
Bodine, Sigrun, and D. A. Lutz. 2009. "Exponentially asymptotically constant systems of difference equations with an application to hyperbolic equilibria." Journal Of Difference Equations And Applications 15(8-9): 821-832.