Synchronization and Control in Modular Networks of Spiking Neurons

In this paper, we consider the dynamics of two types of modular neural networks. The first network consists of two modules of non-interacting neurons while each neuron inhibits all the neurons of an opposite module. We explain the mechanism for emergence of anti-phase group bursts in the network and showed that the collective behavior underlies a regular response of the system to external pulse stimulation. The networks of the second type contain modules with complex topology which are connected by relatively sparse excitatory delayed coupling. We found a dual role of the inter-module coupling delay in the collective network dynamics. First, with increasing time delay, in-phase and anti-phase regimes, where individual spikes form rhythmic modular burst-like oscillations, alternate with each other. Second, the average frequency of the collective oscillations in each of these regimes decreases with increasing inter-module coupling delay.