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arXiv · 2106.12918

Noise induced new quasi-period and periods switching

Yuxuan Wu·Yuxing Jiao·Yanzhen Zhao·Haojun Jia·Liufang Xu
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Abstract

We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure regions. We find that a new quasi-periodic component, which is not allowed by deterministic dynamics, will be generated by noise inducing in the first two regions, and this quasi-period will be more and more stable along with the noise increasing. Especially, in the second region, the quasi-period will compete with a stable limit cycle and perform a new transient rhythm. Furthermore, we ascertain the entropy production rate (EPR) and the heat dissipation rate (HDR), and discover a minimal value with elucidating theoretically. In the end, we unveil the mechanism of the quasi-periods forming, and show a practical biological instance. We expect that this work is helpful to solve some biological or ecological problems, such as genetic origin of periodical cicadas and population dynamics with fluctuation.

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Yuxuan Wu, Yuxing Jiao, Yanzhen Zhao, Haojun Jia, Liufang Xu. 2021-06-24. Noise induced new quasi-period and periods switching. https://doi.org/10.1103/physreve.105.014419

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