Information Theoretic Measures to Infer Feedback Dynamics in Coupled Logistic Networks

Abstract

A process network is a collection of interacting time series nodes, in which interactions can range from weak dependencies to complete synchronization. Between these extremes, nodes may respond to each other or external forcing at certain time scales and strengths. Identification of such dependencies from time series can reveal the complex behavior of the system as a whole. Since observed time series datasets are often limited in length, robust measures are needed to quantify strengths and time scales of interactions and their unique contributions to the whole system behavior. We generate coupled chaotic logistic networks with a range of connectivity structures, time scales, noise, and forcing mechanisms, and compute variance and lagged mutual information measures to evaluate how detected time dependencies reveal system behavior. When a target node is detected to receive information from multiple sources, we compute conditional mutual information and total shared information between each source node pair to identify unique or redundant sources. While variance measures capture synchronization trends, combinations of information measures provide further distinctions regarding drivers, redundancies, and time dependencies within the network. We find that imposed network connectivity often leads to induced feedback that is identified as redundant links, and cannot be distinguished from imposed causal linkages. We find that random or external driving nodes are more likely to provide unique information than mutually dependent nodes in a highly connected network. In process networks constructed from observed data, the methods presented can be used to infer connectivity, dominant interactions, and systemic behavioral shift.

Keywords

• mutual information
• process network
• synchronization
• chaotic logistic equation
• redundancy
• synergy
• induced feedback