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Large Deviations For Synchronized System

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Abstract

We develop the large deviations principle for synchronized system with small noise. Depending on the interaction between the intensity of the noise with coupling strength, we get different behavior. By simple transformations, the original synchronized system is equivalently converted into the slow-fast system, then we derive the representations for the action functional of the slow variables via weak convergence methods. Therefore, the large deviation properties corresponding to the original synchronized system are derived. In particular, we present a large deviation principle for a particular system in view of Smoluchowski–Kramers arguments and study the synchronization of the quasipotential for a linear system.

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Acknowledgements

The authors are grateful to the anonymous reviewer for detailed and valuable comments that help in depth to improve the quality of the paper. The authors also acknowledge the support provided by the Fundamental Research Funds for the Central Universities, HUST: 2016YXMS003 and NSFs of China (Nos. 11271013, 11471340, 10901065).

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  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Ge Li & Jicheng Liu

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  1. Ge Li
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  2. Jicheng Liu
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Correspondence to Jicheng Liu.

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Li, G., Liu, J. Large Deviations For Synchronized System. Appl Math Optim 86, 30 (2022). https://doi.org/10.1007/s00245-022-09889-6

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