This talk is concerned with asymptotic persistence, extinction and spreading properties for a class of reaction--diffusion systems that do not satisfy the comparison principle. These systems appear frequently in models for mathematical biology and, despite the non-monotonicity, share structural and phenomenological properties with the well-known scalar Fisher--KPP equation: the hair-trigger effect, the linear determinacy of planar spreading speeds, the Freidlin--Gärtner formula for radial spreading.
I will first present results established a few years ago on the case of space-time homogeneous coefficients.
Then I will present recent generalizations in the case of space-time periodic coefficients, that involve in particular a more delicate generalized principal spectral theory.
(Séminaire en ligne. Lien zoom: https://cnrs.zoom.us/j/98177403524?pwd=eDZCcVorVFllTi96QWNUd3ZjRm1jZz09)
Romain Duboscq, David Lafontaine