A note on a parameter bound for global stability in the 2D coupled Ricker equation. (English) Zbl 1456.37104
Summary: In prior work on the coupled 2D Ricker Map, a conjecture was made concerning an upper bound on parameters that would guarantee injectivity of the map in a certain region of the plane. This injective property was used to show global asymptotic stability of the coexistent fixed point. In this short note, we find an explicit formula for the optimum upper bounds.
MSC:
| 37N25 | Dynamical systems in biology |
| 39A30 | Stability theory for difference equations |
| 39A12 | Discrete version of topics in analysis |
| 92D25 | Population dynamics (general) |
References:
| [1] | Cabral Balreira, E.; Elaydi, S.; Luis, R., Local stability implies global stability for the planar Ricker competition model, Discrete Contin. Dyn. Syst. Ser. B, 19, 323-351 (2014) · Zbl 1282.39016 |
| [2] | Ryals, B.; Sacker, R., Global stability in the 2D Ricker equation, J. Differ. Equ. Appl., 21, 1068-1071 (2015) · Zbl 1341.39006 |
| [3] | Ryals, B.; Sacker, R., Global stability in the 2D Ricker equation Revisited, Discrete Contin. Dyn. Syst. Ser. B, 22, 2, 585-604 (2017) · Zbl 1362.39024 |
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