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Multiple-node basin stability in complex dynamical networks.

Chiranjit Mitra1,2, Anshul Choudhary3, Sudeshna Sinha3

  • 1Potsdam Institute for Climate Impact Research, Research Domain IV-Transdisciplinary Concepts & Methods, 14412 Potsdam, Germany.

Physical Review. E
|April 19, 2017
PubMed
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We introduce multiple-node basin stability (BS) to measure how robust complex networks are to simultaneous perturbations. This new method quantifies the critical number of nodes that can be disturbed before a system loses stability.

Area of Science:

  • Complex systems
  • Network science
  • Dynamical systems theory

Background:

  • Networked dynamical systems often exhibit multistability, with multiple stable states.
  • The stability of desired states (e.g., synchronization) under large perturbations is crucial for real-world systems like power grids and the brain.
  • Existing methods for quantifying stability may not adequately address perturbations affecting multiple network nodes simultaneously.

Purpose of the Study:

  • To propose a general framework for multiple-node basin stability (BS) to quantify the global stability and robustness of networked dynamical systems.
  • To develop a method for estimating the critical number of simultaneously perturbed nodes that destabilize a system.
  • To provide a tool for identifying nodes critical for system control or protection against perturbations.

Related Experiment Videos

Main Methods:

  • Extending the concept of basin stability (BS) to a multi-node framework.
  • Analyzing the impact of simultaneous perturbations on multiple nodes within a network.
  • Applying the multiple-node BS framework to a scale-free network of Rössler oscillators and a model of the UK power grid.

Main Results:

  • The multiple-node BS framework provides an estimate of the critical number of nodes whose simultaneous perturbation significantly impairs system recovery to a stable state.
  • The methodology can identify the minimum number of nodes requiring control or protection to ensure system operational stability.
  • Demonstrated the utility of multiple-node BS in assessing the stability of synchronized states in complex network models.

Conclusions:

  • Multiple-node BS offers a robust method for assessing the global stability and resilience of networked dynamical systems against nonlocal perturbations.
  • This framework is valuable for understanding system vulnerabilities, optimizing control strategies, and safeguarding critical infrastructure.
  • The approach is applicable to diverse systems, including biological networks, power grids, and neural networks.