Journal Articles

Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/7915

Browse

Author: search.filters.author.Laing CRSubject: search.filters.subject.Neurons

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Periodic solutions in next generation neural field models
    (Springer Nature, 2023-10) Laing CR; Omel'chenko O
    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 solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators
  • Thumbnail Image
    Item
    Learning emergent partial differential equations in a learned emergent space
    (Springer Nature Limited, 2022-06-09) Kemeth FP; Bertalan T; Thiem T; Dietrich F; Moon SJ; Laing CR; Kevrekidis IG
    We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.