Multi-node basin stability in complex dynamical networks

TL;DR

This paper introduces multi-node basin stability, a new framework to evaluate the robustness of complex networks against large, simultaneous perturbations affecting multiple nodes, with applications to power grids and oscillator networks.

Contribution

The paper develops a novel multi-node basin stability framework to quantify global stability and robustness of networked dynamical systems under multi-node perturbations.

Findings

Multi-node BS estimates the critical number of nodes affecting stability.

Framework applied to power grid and oscillator networks.

Provides insights into network robustness and targeted control strategies.

Abstract

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) (Menck et al., Nature Physics 9, 89 (2013)), we propose here the general framework of \emph{multi-node basin stability} for gauging global stability and robustness of networked dynamical systems in response to non-local perturbations simultaneously affecting multiple nodes of a system. The framework of multi-node BS provides an estimate of the critical number of nodes which when simultaneously perturbed, significantly reduces the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multi-node BS can also be utilized for probing the influence of spatially localised perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multi-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of R\"{o}ssler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.