Gaucel, Sébastien; Langlais, Michel Some remarks on a singular reaction-diffusion system arising in predator-prey modeling. (English) Zbl 1213.35257 Discrete Contin. Dyn. Syst., Ser. B 8, No. 1, 61-72 (2007). Summary: This note is dedicated to the question of global existence for solutions to a two component singular system of reaction-diffusion equations modeling predator-prey interactions in insular environments. Depending on a 2D parameter space, positive orbits of the underlying ODE system undergo interesting dynamics, e.g., finite time existence and global existence may coexist. These results are partially extended to the reaction-diffusion system in the case of identical diffusivities. Our analysis relies on an auxiliary non singular reaction-diffusion system whose solutions may or may not blow up in finite time. Numerical simulations illustrate our analysis, including a numerical evidence of spatio-temporal oscillations. Cited in 13 Documents MSC: 35K57 Reaction-diffusion equations 35K52 Initial-boundary value problems for higher-order parabolic systems 92D25 Population dynamics (general) Keywords:Global existence; blow-up time; oscillations; singular reaction-diffusion systems; predator-prey model in insular environment; invasion and persistence PDFBibTeX XMLCite \textit{S. Gaucel} and \textit{M. Langlais}, Discrete Contin. Dyn. Syst., Ser. B 8, No. 1, 61--72 (2007; Zbl 1213.35257) Full Text: DOI