Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

Abstract

Non-autonomous, higher order difference equations of type

with real variables and parameters have appeared frequently in the literature. These equations are well defined on Banach algebras, and existing convergence results can be generalized from real numbers to algebras. Through this generalization and by using a recently obtained semiconjugate factorization of the above equation, new sufficient conditions are obtained for the convergence to zero of all solutions of nonlinear difference equations of the above type. Where reduction of order is possible, these conditions extend the ranges of parameters for which the origin is a global attractor even in the case of real variables and parameters.

Keywords:

• reduction of order
• global attractivity
• non-autonomous
• higher order
• difference equation
• Banach algebra

Keywords:

• 39A10
• 39A30