Esta semana, o PPGMAT está recebendo a visita do prof. Julián López-Gómez, da Universidad Complutense de Madrid (Espanha), pelo projeto CAPEs PrInt.

 

No dia 16/08/2024 ele irá ministrar uma palestra voltada a toda a comunidade acadêmica. Convidamos a todos para participar.

 

Data: 16/08/2024

Horário: 10:30

Local: Auditório MAT/UnB

 

Título: New trends in Lotka-Volterra diffusive competition

Resumo: This talk discusses several recent findings on the dynamics of the spatially-heterogeneous diffusive Lotka-Volterra competing species model. First, it delivers a general (optimal) singular perturbation result generalizing, very substantially, the pioneering theorem of Hutson, López-Gómez, Mischaikow and Vickers (1994) for their mutant model, later analyzed, very sharply, by W. M. Ni and his collaborators.

 

Then, it establishes that, as soon as any steady-state solution of the non-spatial model is linearly unstable somewhere in the inhabiting territory, $\Omega$, any steady state of the spatial counterpart perturbing from it therein as the diffusion rates separate away from zero must be linearly unstable. From this feature one can derive a number of rather astonishing consequences, as the

multiplicity of the coexistence steady states when the non-spatial model exhibits founder control competition somewhere in $\Omega$, say $\Omega_{bi}$, even if $\Omega_{bi}$ is negligible empirically. Actually, this is the first existing multiplicity result for small diffusion rates. 

 

Finally, based on the Picone identity, we can establish a new, rather striking, uniqueness result valid for general spatially heterogeneous models. This result generalizes, very substantially, those of W. M. Ni and collaborators for the autonomous model.