Leeds Applied Nonlinear Dynamics Seminar (two talks)
- Date
- @ MALL, online, 12:00
- Location
- MALL, online
- Speaker 1
- Hil Meijer
- Affiliation
- University of Twente
- Speaker 2
- Davide Liessi
- Affiliation
- University of Udine
Hil Meijer (University of Twente, NL),
Title: Synchrony across the brain; a harmonic balance approach to delay-coupled oscillators
Abstract: Delays are a natural component of computational models of large-scale brain dynamics. Delays combined with local synaptic activity typically lead to oscillations, but the question is whether synchrony or some out-of-phase solution is stable. Here we present a machinery using harmonic balance and accounting for symmetries to look for instabilities of the synchronous solution. We first analyse a simple model on a ring where ``travelling waves'' with activity jumping to the nearest or next-nearest neighbour appear. Employing numerical continuation, we also track which pattern exists as we change the delay. For stability of the asynchronous solutions, we rely on simulations. We then move on to the Wilson-Cowan model with similar results, and highlight some of the additional numerical challenges.
Davide Liessi (University of Udine, IT).
Title: Stability of periodic orbits of delay equations
Abstract: The local stability properties of periodic orbits of a delay differential equation or of a renewal equation can be studied by computing the Floquet multipliers, i.e the eigenvalues of the monodromy operators of the linearized equation. These operators can be approximated via pseudospectral collocation, resulting in a matrix whose eigenvalues can be computed with standard methods. In this seminar I will recall the key ideas of the Floquet theory for delay equations, based on the sun-star perturbation theory, and I will present the pseudospectral approximation method, along with some examples showing its effectiveness.