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Enhancement of early warning properties in the Kuramoto model and in an atrial fibrillation model due to an external perturbation of the system

Author

Listed:
  • David García-Gudiño
  • Emmanuel Landa
  • Joel Mendoza-Temis
  • Alondra Albarado-Ibañez
  • Juan C Toledo-Roy
  • Irving O Morales
  • Alejandro Frank

Abstract

When a complex dynamical system is externally disturbed, the statistical moments of signals associated to it can be affected in ways that depend on the nature and amplitude of the perturbation. In systems that exhibit phase transitions, the statistical moments can be used as Early Warnings (EW) of the transition. A natural question is thus to wonder what effect external disturbances have on the EWs of system. In this work we study the impact of external noise added to the system on the EWs, with particular focus on understanding the importance of the amplitude and complexity of the noise. We do this by analyzing the EWs of two computational models related to biology: the Kuramoto model, which is a paradigm of synchronization for biological systems, and a cellular automaton model of cardiac dynamics which has been used as a model for atrial fibrillation. For each model we first characterize the EWs. Then, we introduce external noise of varying intensity and nature to observe what effect this has on the EWs. In both cases we find that the introduction of noise amplified the EWs, with more complex noise having a greater effect. This both offers a way to improve the chance of detection of EWs in real systems and suggests that natural variability in the real world does not have a detrimental effect on EWs, but the opposite.

Suggested Citation

  • David García-Gudiño & Emmanuel Landa & Joel Mendoza-Temis & Alondra Albarado-Ibañez & Juan C Toledo-Roy & Irving O Morales & Alejandro Frank, 2017. "Enhancement of early warning properties in the Kuramoto model and in an atrial fibrillation model due to an external perturbation of the system," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-14, July.
    • Handle: RePEc:plo:pone00:0181953
    DOI: 10.1371/journal.pone.0181953
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    References listed on IDEAS

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    1. Vasilis Dakos & Stephen R Carpenter & William A Brock & Aaron M Ellison & Vishwesha Guttal & Anthony R Ives & Sonia Kéfi & Valerie Livina & David A Seekell & Egbert H van Nes & Marten Scheffer, 2012. "Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-20, July.
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