Integrability of a Globally Coupled Complex Riccati Array : Quadratic Integrate-and-Fire Neurons, Phase Oscillators, and All in between
(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.
(Less)
- author
- Cestnik, Rok LU and Martens, Erik A. LU
- organization
- publishing date
- 2024-01-29
- type
- 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
- pmid:38364133
- 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
- 2024-08-14 01:58:14
@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}}, }