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New explicit global asymptotic stability criteria for higher order difference equations. (English) Zbl 1186.39022

Summary: New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.

MSC:

39A30 Stability theory for difference equations
39A10 Additive difference equations
92B05 General biology and biomathematics
91B64 Macroeconomic theory (monetary models, models of taxation)
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