Seminar 21 -S3, Tuesday 28th March 2023, 14:00 (London Time)
Speaker: John Andreas Wyller (Norwegian University of Life Sciences -NMBU)
Title: Homogenization theory and neural field models
Abstract: In the last decades great advances have been made in mapping neural circuitry of the brain. This has been facilitated by novel experimental techniques for studies both at the single-cell and systems levels. It still remains, though, to combine all the pieces in the puzzle to a coherent picture of brain function. While single nerve cells (neurons) are fairly well understood, the signal – processing properties of the nerve-cell networks in cortex are still obscure. The growth of experimental data has led to a revival of so – called rate equation models for cell networks in nervous tissue (neural networks). In these models, the probability for firing action potentials, the key information carriers in the brain, is the main dynamical variable. These models assume the form of coupled integral and integro – differential equations, and they describe non-linearand nonlocal interactions between the population of excitatory and inhibitory neurons.
In the present talk I will discuss the properties of the continuum limit of a 2 population nonlocal Hopfield type of neuronal network model, with spatial periodic microstructure incorporated in the connectivity strength. The modelling framework is derived by means of a homogenization procedure, where the spatial nonlocalities are dealt with by means of Visintins theorem for 2-scale convergence of convolution integrals. I will discuss existence and stability of stationary localized solutions (bumps) and pattern formation though Turing type of instabilities within the framework of this model.
Biography: TBA