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  • Letter
  • Open Access

Phase dynamics of noise-induced coherent oscillations in excitable systems

Jinjie Zhu1,2,*, Yuzuru Kato3, and Hiroya Nakao2,†

  • 1School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
  • 2Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
  • 3Department of Complex and Intelligent Systems, Future University Hakodate, Hokkaido 041-8655, Japan

  • *zhu.j.ag@m.titech.ac.jp
  • †nakao@sc.e.titech.ac.jp
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Phys. Rev. Research 4, L022041 – Published 24 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022041

Abstract

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase reduction of the hybrid system to derive an effective, dimensionality-reduced phase equation. We apply the reduced phase model to a periodically forced excitable system and two-coupled excitable systems, both undergoing noise-induced oscillations. The reduced phase model can quantitatively predict the entrainment of a single system to the periodic force and the mutual synchronization of two coupled systems, including the phase slipping behavior due to noise, as verified by Monte Carlo simulations. The derived phase model gives a simple and efficient description of noise-induced oscillations and can be applied to the analysis of more general cases.

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Phys. Rev. Research 4, L022041– Published 24 May, 2022
  • Received 4 April 2022
  • Accepted 12 May 2022
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