Abstract
Persistence and stability properties are considered for a class of forced positive nonlinear delay-differential systems which arise in mathematical ecology and other applied contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes in an ecological setting), disturbances induced by seasonal or environmental variation, or migration. We provide necessary and sufficient conditions under which the states of these models are semi-globally persistent, uniformly with respect to the initial conditions and forcing terms. Under mild assumptions, the model under consideration naturally admits two steady states (equilibria) when unforced: the origin and a unique non-zero steady state. We present sufficient conditions for the non-zero steady state to be stable in a sense which is reminiscent of input-to-state stability, a stability notion for forced systems developed in control theory. In the absence of forcing, our input-to-sate stability concept is identical to semi-global exponential stability.
Original language | English |
---|---|
Article number | 1 |
Journal | Acta Applicandae Mathematicae |
Volume | 174 |
Issue number | 1 |
Early online date | 21 Jun 2021 |
DOIs | |
Publication status | Published - 31 Aug 2021 |
Bibliographical note
Funding Information:D. Franco was supported by grant MTM2017-85054-C2-2-P (AEI/FEDER, UE) and ETSII-UNED grant 2021-MAT10.
Funding
D. Franco was supported by grant MTM2017-85054-C2-2-P (AEI/FEDER, UE) and ETSII-UNED grant 2021-MAT10.
Keywords
- Delay-differential systems
- Density-dependent population models
- Environmental forcing
- Forced systems
- Input-to-state stability
- Persistence
- Positive systems
- Semi-global exponential stability
ASJC Scopus subject areas
- Applied Mathematics