Cluster Synchronization in Boolean Neural Networks

Abstract

This chapter focuses on the dynamics of spiking neural networks built with the Boolean neurons introduced in Chap. 8. I first introduce preceding work on the dynamics of spiking neural networks with realistic neuron models in Sect. 9.1 and discuss the master stability function and the tool of the greatest common divisor (GCD) in Sect. 9.2. Then, I present experimental results of the dynamics of networks of Boolean neurons in Sects. 9.3–9.7. Specifically, I show the occurrence of cluster synchronization, which is a network dynamics where the network can be separated into groups of synchronized dynamics, where nodes from different groups are not synchronized. This state is achieved in interconnected ring networks of Boolean neurons (Sect. 9.3), breaks down under certain scalings of internal timescales (Sects. 9.4 and 9.5), and can be controlled using a small number of nodes in the network (Sect. 9.6) (Results of this chapter are published in reference Rosin et al. Phys Rev Lett 110:104102, 2013.). These results are also reproduced with a model (Sect. 9.7).