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A Class of Second Order Difference Equations Inspired by Euler’s Discretization Method

H. Sedaghat, H. Shojaei

Abstract


In this paper we study a multiparameter, nonlinear second order difference equation that is motivated by the Euler discretization of derivatives in the autonomous, second order differential equation derived from Newton’s second law in mechanics. Our objective is mainly to analyze qualitative properties of the second order difference equation such as convergence, periodicity and chaos. With proper restrictions, two different semiconjugate factorizations facilitate our work.

Keywords


Euler’s forward method, difference equation, global stability, persistent oscillations, periodicity, chaos, semiconjugates

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