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Cluster Synchronization in Boolean Neural Networks

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Book cover Dynamics of Complex Autonomous Boolean Networks

Part of the book series: Springer Theses ((Springer Theses))

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).

The main contribution of this chapter are:

  • realizing experimentally networks of 32 Boolean neurons showing cluster synchronization on a logic chip;

  • pointing out limitations—specifically a breakdown—of a common network theory for cluster synchronization;

  • discovering of a control mechanism of cluster network dynamics.

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Notes

  1. 1.

    This section is written in accordance with Ref. [38].

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  1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany

    David P. Rosin

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Correspondence to David P. Rosin .

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Rosin, D.P. (2015). Cluster Synchronization in Boolean Neural Networks. In: Dynamics of Complex Autonomous Boolean Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-13578-6_9

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