Abstract
A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.
Highlights
As one aims at finding a functional network that resembles as close as possible the physical connectivity of the system, it is crucial to develop reliable techniques capable of unveiling interdependencies, based on the observation of the dynamics of the units that compose the system
We have analysed the relation between inferred functional networks and the underlying structural networks in two different systems, a simulated set of Kuramoto oscillators and an experimental set of Rössler chaotic electronic circuits
We focused in the dependence on the strength of the interaction among the system components, in the similarity measure used, and in the type of variable analysed
Summary
As one aims at finding a functional network that resembles as close as possible the physical connectivity of the system, it is crucial to develop reliable techniques capable of unveiling interdependencies, based on the observation of the dynamics of the units that compose the system. In7 a system composed by discrete-time units was studied (various maps were considered, including the Logistic and Circle maps) and it was found that (i) under appropriated coupling conditions the network can be perfectly inferred, these conditions being a weak coupling regime where the network is neither fully synchronized, nor completely desynchronized and (ii) regarding the statistical similarity measure used for inferring the system structural connectivity, the mutual information in general outperforms the cross-correlation. We test these observations by considering a set of phase oscillators and a set of chaotic three-dimensional oscillators. To perform our analysis, we use synthetic data generated via model simulations, and test the methods with experimental data recorded from a real system of interacting electronic circuits
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