Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs

TL;DR

This paper introduces a self-organized, stochastic mechanism for explosive synchronization in complex networks, revealing structural signatures and demonstrating control in both oscillatory and biological systems, with analytical insights into the transitions.

Contribution

It presents a novel self-organized process for explosive synchronization, combining local rules and stochastic optimization, applicable to diverse systems including neural and power-grid networks.

Findings

Identification of structural features like frequency-degree correlations and disassortative patterns.

Demonstration of explosive transitions in both periodic and chaotic oscillator models.

Analytical characterization of transitions using collective coordinates and Ott-Antonsen ansatz.

Abstract

We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or a few links. Here we build a self-organized and stochastic version of these bombs, by optimizing global synchrony with decentralized information in a competitive link-percolation process driven by a local rule. We find explosive fingerprints on the emerging network structure, including frequency-degree correlations, disassortative patterns and a delayed percolation threshold. We show that these bomb-like transitions can be designed both in systems of Kuramoto -- periodic -- and R\"ossler -- chaotic -- oscillators and in a model of cardiac pacemaker cells. We analytically characterize the transitions in the Kuramoto case by combining a precise collective coordinates approach and the Ott-Antonsen ansatz. Furthermore, we study the robustness of the phenomena under changes in the main parameters and the unexpected effect of optimal noise in our model. Our results propose a minimal self-organized mechanism of network growth to understand and control explosive synchronization in adaptive biological systems like the brain and engineered ones like power-grids or electronic circuits. From a theoretical standpoint, the emergence of synchronization explosions and bistability induced by localized structural perturbations -- without any fine-tuning of global parameters -- joins explosive synchronization and percolation under the same mechanistic framework.