660 research outputs found
Asymptotic behaviour for a class of non-monotone delay differential systems with applications
The paper concerns a class of -dimensional non-autonomous delay
differential equations obtained by adding a non-monotone delayed perturbation
to a linear homogeneous cooperative system of ordinary differential equations.
This family covers a wide set of models used in structured population dynamics.
By exploiting the stability and the monotone character of the linear ODE, we
establish sufficient conditions for both the extinction of all the populations
and the permanence of the system. In the case of DDEs with autonomous
coefficients (but possible time-varying delays), sharp results are obtained,
even in the case of a reducible community matrix. As a sub-product, our results
improve some criteria for autonomous systems published in recent literature. As
an important illustration, the extinction, persistence and permanence of a
non-autonomous Nicholson system with patch structure and multiple
time-dependent delays are analysed.Comment: 26 pages, J Dyn Diff Equat (2017
Permanence and exponential stability for generalised nonautonomous Nicholson systems
The paper is concerned with nonautonomous generalised Nicholson systems under conditions which imply their permanence: by refining the assumptions for permanence, explicit lower and upper uniform bounds for all positive solutions are provided, as well as criteria for the global exponential stability of these systems. In particular, for periodic systems, conditions for the existence of a globally exponentially attractive positive periodic solution are derived
- …