Distinguishing Direct from Indirect Interactions in Oscillatory Networks with Multiple Time Scales

Abstract

We propose a method to infer the coupling structure in networks of nonlinear oscillatory systems with multiple time scales. The method of partial phase synchronization allows us to infer the coupling structure for coupled nonlinear oscillators with one well-defined time scale. The case of oscillators with multiple time scales has remained a challenge until now. Here, we introduce partial recurrence based synchronization analysis to tackle this challenge. We successfully apply the proposed method to model systems and experimental data from coupled electrochemical oscillators. The statistical significance of the results is evaluated based on a surrogate hypothesis test.

Dynamics of electrochemical oscillators with electrode size disparity: asymmetrical coupling and anomalous phase synchronization

“…41,42 The dual oscillator setup with different electrode sizes can be extended to build small sets (e.g. three locally coupled 69,70 ) or large population 21,25 of electrochemical oscillators with asymmetrical coupling. These networks could provide information about dynamical behavior related, for example, to other anomalous phase synchronization effects (e.g.…”

Nonlinear Granger causality and its application in the analysis of epileptic EEG and ECG signal

“…The EEG reflects the computer activity and functional status of brain tissue [2]. The change of ECG signal in the regulation of autonomic nerve and the evaluation of autonomic nerve function which has better specificity and sensitivity than other physiological parameters [3].…”

Information theoretical methods for complex network structure reconstruction

“…Methods for direct and indirect interactions assessment found in the reviewed literature were designed ad hoc for too dense or too small networks (Nawrath et al 2010;Yan et al 2007), and most of them require additional information in order to estimate or tune parameters to differentiate the two kinds of interactions (Chua et al 2008;Yan et al 2007). Noteworthy is to say, a great deal of importance was expressed in direct and indirect interactions assessment, regardless the particular field of research (Systems Biology, Economics or Ecology).…”

“…Noteworthy is to say, a great deal of importance was expressed in direct and indirect interactions assessment, regardless the particular field of research (Systems Biology, Economics or Ecology). Most efforts invested in distinguishing between these two kinds of interactions among nodes were either done manually (for instance, see (Beltrán et al 2012;Callaway and Howard 2007)) or rely on extremely specific issues of the underlying networks (Baldazzi et al 2010;Nawrath et al 2010), hence the relevance of the method we introduce in this paper.…”