A note on dissipativity and permanence of delay difference equations

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 i...

Full description

Saved in:
Bibliographic Details
Main Author: Garab Ábel
Format: Serial
Published: 2018
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet - késleltetett
doi:10.14232/ejqtde.2018.1.51

Online Access:http://acta.bibl.u-szeged.hu/58134
Description
Summary: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.
Physical Description:1-12
ISSN:1417-3875