Ernest Montbrió — Center for Brain and Cognition - Universitat Pompeu Fabra Barcelona #
Synchronization patterns in firing rate models with synaptic delay #
Population models of neuronal activity have become an standard tool of analysis in computational neuroscience. Rather than focus on the microscopic dynamics of neurons,  these models describe the collective properties of large numbers of neurons, typically in terms of the mean firing rate of a neuronal ensemble. In general, such population models, often called firing rate equations (FRE) are obtained using heuristic mean-field arguments. Despite their heuristic nature, Heuristic-FRE often show remarkable qualitative agreement with the dynamics in equivalent networks of spiking neurons. However, this agreement breaks down once a significant fraction of the  neurons in the population fires spikes synchronously. In my presentation, I will introduce a recent theory to derive the exact FRE for a large population of heterogeneous Quadratic Integrate and Fire (QIF) neurons. In contrast with traditional H-FRE, these QIF-FRE adequately capture collective synchronization. To illustrate this, I will use the QIF-FRE to investigate the emergence of synchronous oscillations in a population of identical inhibitory neurons with synaptic delays. The analysis reveals the presence of an intriguing class of partially synchronized states, which display periodic and even chaotic collective dynamics. Finally, the relationship of the model’s dynamics with fast neuronal oscillations will be discussed.