Global stability in the Ricker model with delay and stocking
- Ziyad AlSharawi,
- Sadok Kallel
Sadok Kallel
American University of Sharjah College of Arts and Sciences
Author ProfileAbstract
In this paper, we consider the Ricker model with delay and constant or
periodic stocking. The impact of delay and stocking on stability is
known to reflect opposing effect, which motivates investigating the
interaction between these factors and their influence on overall
stability. We found that the high stocking density tends to neutralize
the delay effect. Conditions are established on the parameters in order
to guarantee the global stability of the equilibrium solution in the
case of constant stocking, as well as the global stability of the
2-periodic solution in the case of 2-periodic stocking. Our approach
extensively relies on the utilization of the embedding technique.
Whether constant stocking or periodic stocking, the mode has the
potential to undergo a Neimark-Sacker bifurcation in both cases.
However, the Neimark-Sacker bifurcation in the 2-periodic case results
in the emergence of two invariant curves that collectively function as a
single attractor. Finally, we pose open questions in the form of
conjectures about global stability for certain choices of the
parameters.22 Oct 2023Submitted to Mathematical Methods in the Applied Sciences 24 Oct 2023Submission Checks Completed
24 Oct 2023Assigned to Editor
02 Nov 2023Review(s) Completed, Editorial Evaluation Pending
06 Nov 2023Reviewer(s) Assigned
31 Jan 20241st Revision Received
05 Feb 2024Submission Checks Completed
05 Feb 2024Assigned to Editor
05 Feb 2024Review(s) Completed, Editorial Evaluation Pending
21 Jul 2024Editorial Decision: Revise Major
29 Jul 20242nd Revision Received
29 Jul 2024Submission Checks Completed
29 Jul 2024Assigned to Editor
29 Jul 2024Review(s) Completed, Editorial Evaluation Pending
31 Jul 2024Reviewer(s) Assigned
10 Aug 2024Editorial Decision: Accept