Phase autoencoder for limit-cycle oscillators

• URL: http://arxiv.org/abs/2403.06992v1
• Date: Wed, 28 Feb 2024 06:03:55 GMT
• Title: Phase autoencoder for limit-cycle oscillators
• Abstract summary: We present a phase autoencoder that encodes the phase of a limit-cycle oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.

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