Feedback percolation on complex networks

TL;DR

This paper introduces feedback percolation, a dynamic framework where local activation probabilities depend on the global giant component size, leading to diverse behaviors like oscillations and chaos not seen in classical models.

Contribution

It presents a unified feedback-based percolation model that captures complex phenomena such as explosive transitions and oscillations in network systems.

Findings

Feedback mechanisms induce hybrid and explosive transitions.

System exhibits limit-cycle oscillations and chaos.

Feedback explains phenomena like systemic collapse and self-regulation.

Abstract

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified framework that dynamically couples the microscopic activation probability to the macroscopic size of the giant component. We show that this simple feedback mechanism produces a rich variety of behaviors both analytically and numerically. Depending on the feedback functions, the system exhibits explosive discontinuous jumps, hybrid transitions, limit-cycle oscillations, and routes to chaos, absent in classical percolation. Our findings establish that macroscopic feedback provides a unifying physical mechanism for phenomena ranging from self-regulating oscillations to systemic infrastructure collapse.