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Global asymptotic stability for minimum-delay difference equations. (English) Zbl 1244.39013

Authors’ abstract: We consider equations of the form

y n =min{f(y n-k 1 ,y n-m 1 ),...,f(y n-k L ,y n-m L )}·

Conditions on f and {(k i ,m i )} which guarantee global asymptotic stability of positive solutions are provided. The results generalize recent work in the literature for equations of the form y n =f(y n-k 1 ,y n-m 1 ). Asymptotic periodicity for solutions is also considered.

MSC:
39A30Stability theory (difference equations)
39A10Additive difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)
39A23Periodic solutions (difference equations)