Information-theoretic description of a feedback-control Kuramoto model
arxiv(2024)
摘要
Semantic Information Theory (SIT) offers a new approach to evaluating the
information architecture of complex systems. In this study we describe the
steps required to operationalize SIT via its application to dynamical
problems. Our road map has four steps: (1) separating the dynamical system into
agent-environment sub-systems; (2) choosing an appropriate coarse graining and
quantifying correlations; (3) identifying a measure of viability; (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 new 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 in in a novel computational (information theoretic)
perspective, where the agent-environment dynamics can be thought of as
analyzing a communication channel. For the former we find that all the
information in our system is semantic. This is in contrast to previous SIT
studies of foragers in which semantic thresholds where seen above which no
further semantic content was obtained.
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