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Global stability in the Ricker model with delay and stocking
  • Ziyad AlSharawi,
  • Sadok Kallel
Ziyad AlSharawi
American University of Sharjah College of Arts and Sciences

Corresponding Author:[email protected]

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Sadok Kallel
American University of Sharjah College of Arts and Sciences
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Abstract

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