| Abstract: |
| In 1998, Dockery et al. showed that for two competing species which are identical except for their diffusion rate, the slower diffuser can exclude the faster counterpart regardless of initial data. It is then conjectured that the same result holds for N competing species, for any number N greater than or equal to 3. In this talk, we will discuss some recent progress towards a generalized reduction principle based on new estimates of the underlying principal Floquet bundle. Our discussion includes the case when the coefficients are autonomous, time-periodic, or more general non-autonomous coefficients under spatially heterogeneous conditions. This is joint work with Robert S. Cantrell and Yuan Lou. |
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