Mathematical modelling of stability and dynamics of localized activity in biological cell networks

In the last decades great advances have been made in mapping the 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 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 reviv al of so-called rate models for cell networks in nervous tissue (neural networks). In these field 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-line ar, non-local interactions between different neuron populations. The present project focuses on the study of mathematical and numerical aspects of rate models including inhibitory as well as excitatory neural populations. Both qualitative analytical methods and simulations based on advanced numerical methods are employ ed. The results are compared with on-going experiments carried out by a collaborating research group at Harvard-MGH in Boston.