STDP in Oscillatory Recurrent Networks: TheoreticalConditions for Desynchronization and Applications to Deep-Brain Stimulation.

Highly synchronized neural networks can be the source of various pathologies such as Parkinson's disease or essential tremor. Therefore, it is crucial to better understand the dynamics of such networks and the conditions under which a high level of synchronization can be observed. One of the key factors that influences the level of synchronization is the type of learning rule that governs synaptic plasticity. Most of the existing work on synchronization in recurrent networks with synaptic plasticity are based on numerical simulations and there is a clear lack of a theoretical framework for studying the effects of various synaptic plasticity rules. In this paper we derive analytically the conditions for spike-timing dependent plasticity (STDP) to lead a network into a synchronized or a desynchronized state. We also show that under appropriate conditions bistability occurs in recurrent networks governed by STDP. Indeed, a pathological regime with strong connections and therefore strong synchronized activity, as well as a physiological regime with weaker connections and lower levels of synchronization are found to coexist. Furthermore, we show that with appropriate stimulation, the network dynamics can be pushed to the low synchronization stable state. This type of therapeutical stimulation is very different from the existing high-frequency stimulation for deep brain stimulation since once the stimulation is stopped the network stays in the low synchronization regime