A note on dissipativity and permanence of delay difference equations

Garab, Ábel: A note on dissipativity and permanence of delay difference equations. Electronic journal of qualitative theory of differential equations 51. pp. 1-12. (2018)

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Abstract

We give sufficient conditions on the uniform boundedness and permanence of non-autonomous multiple delay difference equations of the form xk+1 = xk fk (xk−d , . . . , xk−1 , xk where fk : D ⊆ (0, ∞) d+1 → (0, ∞). Moreover, we construct a positively invariant absorbing set of the phase space, which implies also the existence of the global (pullback) attractor if the right-hand side is continuous. The results are applicable for a wide range of single species discrete time population dynamical models, such as (non-autonomous) models by Ricker, Pielou or Clark.

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