Phase Reduction and Synchronization of Coupled Noisy Oscillators

Zahra Aminzare; Vaibhav Srivastava

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Phase Reduction and Synchronization of Coupled Noisy Oscillators

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Phase Reduction and Synchronization of Coupled Noisy Oscillators

Zahra Aminzare and Vaibhav Srivastava

ArXiv.org

03/07/2021

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https://arxiv.org/abs/2103.04492View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any internal fluctuations, and (2) a coupling noise which is generated by interactions with other systems. After providing sufficient conditions that foster synchronization in networks of general noisy systems, we focus on weakly coupled networks of noisy oscillators and, using the first- and second-order phase response curves (PRCs), we derive a reduced order stochastic differential equation to describe the corresponding phase evolutions. Finally, we derive synchronization conditions based on the PRCs and illustrate the theoretical results on a couple of models.

Details

Title: Subtitle: Phase Reduction and Synchronization of Coupled Noisy Oscillators
Creators: Zahra Aminzare
Vaibhav Srivastava
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Language: English
Date posted: 03/07/2021
Academic Unit: Mathematics; Iowa Neuroscience Institute
Record Identifier: 9984065771702771

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