A note on dissipativity and permanence of delay difference equations

摘要

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.