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Integrability of a Globally Coupled Complex Riccati Array : Quadratic Integrate-and-Fire Neurons, Phase Oscillators, and All in between

Cestnik, Rok LU and Martens, Erik A. LU orcid (2024) In Physical Review Letters 132(5).
Abstract

We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [Integrability of a globally coupled oscillator array, Phys. Rev. Lett. 70, 2391 (1993).PRLTAO0031-900710.1103/PhysRevLett.70.2391] for sinusoidally coupled phase oscillators and seamlessly includes quadratic integrate-and-fire neurons as the real-valued special case. This simple formulation reshapes our understanding of a broad class of coupled systems - including a particular class of phase-amplitude oscillators - which newly fall under the category of integrable systems. Precise and rigorous analysis of complex Riccati arrays is now within reach, paving a way... (More)

We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [Integrability of a globally coupled oscillator array, Phys. Rev. Lett. 70, 2391 (1993).PRLTAO0031-900710.1103/PhysRevLett.70.2391] for sinusoidally coupled phase oscillators and seamlessly includes quadratic integrate-and-fire neurons as the real-valued special case. This simple formulation reshapes our understanding of a broad class of coupled systems - including a particular class of phase-amplitude oscillators - which newly fall under the category of integrable systems. Precise and rigorous analysis of complex Riccati arrays is now within reach, paving a way to a deeper understanding of emergent behavior of collective dynamics in coupled systems.

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Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
132
issue
5
article number
057201
publisher
American Physical Society
external identifiers
  • scopus:85183982891
ISSN
0031-9007
DOI
10.1103/PhysRevLett.132.057201
language
English
LU publication?
yes
id
1c6faf9d-9ab3-4ad2-9360-f1d65ec08aa7
date added to LUP
2024-02-19 12:09:25
date last changed
2024-02-28 13:45:05
@article{1c6faf9d-9ab3-4ad2-9360-f1d65ec08aa7,
  abstract     = {{<p>We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [Integrability of a globally coupled oscillator array, Phys. Rev. Lett. 70, 2391 (1993).PRLTAO0031-900710.1103/PhysRevLett.70.2391] for sinusoidally coupled phase oscillators and seamlessly includes quadratic integrate-and-fire neurons as the real-valued special case. This simple formulation reshapes our understanding of a broad class of coupled systems - including a particular class of phase-amplitude oscillators - which newly fall under the category of integrable systems. Precise and rigorous analysis of complex Riccati arrays is now within reach, paving a way to a deeper understanding of emergent behavior of collective dynamics in coupled systems.</p>}},
  author       = {{Cestnik, Rok and Martens, Erik A.}},
  issn         = {{0031-9007}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{5}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Letters}},
  title        = {{Integrability of a Globally Coupled Complex Riccati Array : Quadratic Integrate-and-Fire Neurons, Phase Oscillators, and All in between}},
  url          = {{http://dx.doi.org/10.1103/PhysRevLett.132.057201}},
  doi          = {{10.1103/PhysRevLett.132.057201}},
  volume       = {{132}},
  year         = {{2024}},
}