Information-theoretic description of a feedback-control Kuramoto model

Semantic information theory (SIT) offers an alternative approach to evaluating the information architecture of complex systems. In this paper, we describe the steps required to SIT via its application to dynamical problems. Our road map has four steps: (1) separating the dynamical system into agent-environment subsystems, (2) choosing an appropriate coarse graining and quantifying correlations, (3) identifying a measure of viability, and (4) implementing a scrambling protocol and measuring the semantic content. We apply the road map to a model inspired by the neural dynamics of epileptic seizures whereby an agent (a control process) attempts to maintain an environment (a base process) in a desynchronized state. The synchronization dynamics is studied through the well-known Kuramoto model of phase synchronization. Our application of SIT to this problem reveals features of both semantic information and the Kuramoto model. For the latter, we find articulating the correlational structure for agent and environment (the oscillators) allows us to cast the model from a computational (information theoretic) perspective, where the agent-environment dynamics form a communication channel. For the former, we find a topological dependence of whether information can be considered semantic or not. Published by the American Physical Society 2024