«An existence result for a degenerate cross-diffusion system»
Conferenciante: Havva Yoldas (T.U. Delft)
Hora: 10:00h
Resumen: We look at a cross-diffusion system consisting of two Fokker-Planck equations where the gradient of the density for each species acts as a potential for the other one. It is a degenerate system in the sense that it loses its parabolic behavior on some part of the domain. However, the system is also the gradient flow for the Wasserstein distance of a functional which is not lower semicontinuous. We then compute the convexification of the integrand (thus the lower semi continuous envelope of the functional) and provide an existence result in a suitable sense for the gradient flow of the corresponding relaxed functional. This is a joint work with R. Ducasse (Paris) and F. Santambrogio (Lyon).
«Noise-driven bifurcations in a neural field system modelling networks of grid cells»
Conferenciante: José Antonio Carrillo (University of Oxford)
Hora:11:00h
Resumen: In this talk I will review several results in the modelling of grid cells. The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity generated by networks of grid cells emerge from the instability of homogeneous activity for small levels of noise. This is carried out by upscaling a noisy grid cell model to a system of partial differential equations in order to analyse the robustness of network activity patterns with respect to noise. This is rigorously achieved by mean-field type arguments. Inhomogeneous network patterns are numerically understood as branches bifurcating from unstable homogeneous states for small noise levels. We prove that there is a phase transition occurring as the level of noise decreases. Our numerical study also indicates the presence of hysteresis phenomena close to the precise critical noise value. This talk is a summary of four papers/preprints in collaboration with A. Clini, H. Holden, P. Roux and S. Solem.
- Fecha: Jueves, 21 de Diciembre de 2023
- Lugar: Aula A20, Facultad de Ciencias
- Horario: de 10:00 a 12:00
- Organiza: IMAG – Instituto de Matemáticas
- Más información: imag@ugr.es