An a priori study for the reconstruction of some variables of interest in nonlinear complex networks with an application in neuroscience

Many real-life problems can be modeled as a complex network made up of nodes whose dynamics are governed by nonlinear differential equations. State reconstruction of such networks is one fundamental problem consisting in the ability of reconstructing the states of all/some target nodes from the knowledge of some node states. In the framework of networks of nonlinear systems with linear and/or nonlinear couplings, we present a new approach for studying the reconstruction of variables of interest for target nodes. The proposed method is based on a mathematical result ensuring the existence of specific local relations obtained from the governing equations of each node. Two consequences in terms of reconstruction are deduced from this theoretical result and are used to elaborate an algorithm. This algorithm determines the sets of nodes ensuring the reconstruction of the relevant variables of a given target set. We exemplify our approach on a biological neural network of C. elegans, made up of Hodgkin–Huxley type models coupled through linear and nonlinear terms. This provides a testable hypothesis that is likely to improve the analysis of the biological circuitry in C. elegans.