Information-Stable Orbits on Networks with Edge-Level Environmental Feedback

Define a mesoscopic notion of information stability for periodic orbits on graphs: an orbit is “information-stable” if, aggregated by community or motif, the total payoff advantage against evolving mutants exceeds the mutants’ self-play, measured via relative entropy across the trajectory. Incorporate edge-specific environmental feedback. This extends Bhattacharjee et al.’s concept from well-mixed two-strategy systems to networked eco-evolutionary systems exhibiting anti-synchronous oscillations, multistability, and bifurcations not captured by standard ESS logic. It reinterprets anti-synchronous community oscillations as candidates for information-stable orbits and links their existence and stability to network statistics and update rules. This provides a general stability certificate for cycles crucial in eco-evolutionary contexts and yields testable predictions about cycle persistence under perturbations. The impact is a unified conceptual tool to diagnose and design cyclic coexistence in structured ecological communities.

References:

1. Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective.. Sayak Bhattacharjee, V. Dubey, Archan Mukhopadhyay, S. Chakraborty (2022). Physical Review E.