Mean Field Limits and Short-Term Synaptic Facilitation in Continuous Time Models

This chapter, building on the results of Chap. 5 , shows how the behavior of a system of interacting point processes can be described by a system of ordinary differential equations, by studying the mean field limit of large systems of interacting Hawkes processes in a mean field frame. Very interesting phenomena, akin to metastability, appear when short-term synaptic plasticity is included in our models. Short-term facilitation leads, in the mean field limit, to a system of ordinary differential equations that can exhibit several fixed points. With proper parameter choice, one of these fixed points can be interpreted as describing the state of a sub-network of neurons recorded from the prefrontal cortex while animals perform working memory tasks.