289 citations · 1.2k across the 20 of their papers we have counts for
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Periodic solutions in next generation neural field models
Carlo R. Laing, Oleh E. Omel'chenko
We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic…
Explosive behaviour in networks of Winfree oscillators
Shawn Means, Carlo Laing
We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are consi…
Global and Local Reduced Models for Interacting, Heterogeneous Agents
Thomas N. Thiem, Felix P. Kemeth, Tom Bertalan +2
Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics…
Learning emergent PDEs in a learned emergent space
Felix P. Kemeth, Tom Bertalan, Thomas Thiem +4
We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergen…
Emergent spaces for coupled oscillators
Thomas N. Thiem, Mahdi Kooshkbaghi, Tom Bertalan +2
In this paper we present a systematic, data-driven approach to discovering "bespoke" coarse variables based on manifold learning algorithms. We illustrate this methodology with the…
Moving bumps in theta neuron networks
Carlo R. Laing, Oleh Omel'chenko
We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable "bumps" of activity, which move along the ring i…