Dia: Dimecres, 4 de març de 2020
Lloc: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Alberto Pérez-Cervera, Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences
Títol: Accurate mathematical tools for the phase control of biological oscillators
Resum: In this talk we present a numerical methodology for an accurate computation of the phase dynamics of a n-dimensional oscillator. Indeed, we compute the phase dynamics of an oscillator not just on its asymptotic state but also on its transient states. The methodology relies on the parameterization method which allows us to obtain a parameterization of the attracting invariant manifold of a limit cycle in terms of the phase amplitude variables. The talk will highlight the many advantages of computing this parameterization. On the one hand, it permits to compute two important foliations of the attracting manifold of the limit cycle: the isochrons and the isostables which provide a geometrical portrait of the oscillator. On the other hand, it also provides the infinitesimal Phase (Amplitude) Response Functions (iPRFs, (iARFs)), which describe the phase and amplitude dynamics beyond the asymptotic state. The computation of the iPRFs and iARFs, permits to extend the classical adjoint equation for points beyond the limit cycle and allow us to study useful strategies to reduce the dimension of dynamics when applying external perturbations without losing accuracy. We illustrate our methods by applying them to different single neuron and population models in neuroscience.
This is a joint work with my PhD advisors Gemma Huguet and Tere M.Seara
Last updated: Fri Mar 6 12:22:52 2020