Eur. Phys. J. Special Topics 225, 1255-1269 (2016)
https://doi.org/10.1140/epjst/e2016-02670-3

Regular Article

Dynamical complexity in the C.elegans neural network

¹ Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Essex CO4 3SQ, UK
² Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
³ Center for Research and Applications of Nonlinear Systems, Department of Mathematics, University of Patras, Patras 26500, Greece

Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016

Abstract

We model the neuronal circuit of the C.elegans soil worm in terms of a Hindmarsh-Rose system of ordinary differential equations, dividing its circuit into six communities which are determined via the Walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and the Φ_AR auto-regressive integrated information theory measure. We show that Φ_AR provides a useful measure of the information contained in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans brain dynamic network generates more information than the sum of its constituent parts, and that attains higher levels of integrated information for couplings for which either all its communities are highly synchronized, or there is a mixed state of highly synchronized and desynchronized communities.