Lyapunov functions for a Reaction-Diffusion model of Leslie-Gower type
DOI:
https://doi.org/10.5540/03.2026.012.01.0303Palabras clave:
Global Stability, Lyapunov Function, Leslie Gower Model, Reaction-Diffusion, Predator-PreyResumen
The aim of this work is to construct Lyapunov functions to extend the global stability results of a Leslie-Gower reaction-diffusion model in a bounded domain Ω ∈ Rⁿ, with no-flux boundary condition. We extended the global stability results to other parameter regions of the reaction-diffusion model using these Lyapunov functions.
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D. Y. Du and S. B. Hsu. “A diffusive predator-prey model in heterogeneous environment.” In: Journal of Differential Equations 203 (2004), pp. 331–364. doi: 10.1016/j.jde.2004.05.010.
S. B. Hsu. “A survey of constructing Lyapunov functions for mathematical models in population biology.” In: Taiwanese Journal of Mathematics 9 (2005), pp. 151–173. doi: 10.11650/twjm/1500407791.
P. H. Leslie. “Some further notes on the use of matrices in population mathematics”. In: Biometrika 35 (1948), pp. 213–245. doi: 10.2307/2332342.
P. H. Leslie and J. C. Gower. “The properties of a stochastic model for the predator-prey type of interaction between two species”. In: Biometrika 47 (1960), pp. 219–234. doi: 10.1093/biomet/47.3-4.219.
Y. W. Qi and Y. Zhu. “Global stability of Lesile-type predator-prey model.” In: Methods and Applications of Analysis 23 (2016), pp. 259–268. doi: 10.4310/MAA.2016.v23.n3.a3.
R. Redheffer, R. Redlinger, and W. Walter. “A Theorem of La Salle- Lyapunov type for parabolics systems.” In: SIAM Journal on Mathematical Analysis. 19 (1988), pp. 121–132. doi: 10.1137/0519009.
W. Zou and X. Wei. “Global stability in a diffusive predator–prey model of Leslie–Gower type.” In: Partial Differential Equations in Applied Mathematics. 7 (2023), pp. 1–5. doi: 10.1016/j.padiff.2022.100472.