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.