Seminar: Phase Amplitude reduction of Oscillatory dynamics.

Abstract: In this talk we aim to introduce a methodology providing an accurate description of oscillatory dynamics. From the mathematical perspective, oscillations correspond to attracting limit cycles in the phase space whose dynamics can be described by a single variable: the phase. For attracting limit cycles, the orbit of each point on the basin of attraction approaches asymptotically the orbit of a point on the limit cycle. Therefore, we can assign to each point on the basin of attraction of the cycle an asymptotic phase corresponding to the phase of the point on the cycle whose orbit approaches to. By doing this, we can define the isochrons of a cycle as the sets of points having the same asymptotic phase. As we will show during the talk, the isochron distribution allows for a geometrical understanding of the phase shifts caused by external perturbations. This understanding is completed by means of the Phase Response Curves.

As we will describe during the talk, although the usage of the phase variable is quite extended, it has some limitations. To overcome these limitations, an alternative strategy which has gained a lot of interest in the recent years, consists in introducing extra variables, denoted as amplitude variables, which describe the dynamics along the directions transversal to the limit cycle. The addition of these variables allows to describe the effects of the perturbations acting during the transient states in which trajectories have not relaxed yet to the limit cycle.

In this talk we will introduce these phase-amplitude tools providing an accurate geometrical and dynamical description of oscillatory dynamics.

This is a joint work with my PhD advisors: Gemma Huguet and Tere M.Seara from Universitat Politècnnica de Catalunya.

Author: Alberto Pérez-Cervera  (Higher School of Economics – Moscow – Russia).

Date: 16 December 2020

Time: 15:00 h

Link here