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Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise

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Abstract

We study asymptotic stability of a class of non-autonomous stochastic delay lattice systems driven by a multiplicative white noise. Under certain conditions, we prove such systems have a unique tempered complete quasi-solution which exponentially pullback attracts all solutions starting from a tempered random set. When the non-autonomous deterministic forcings are time-periodic, we obtain the existence, uniqueness and exponential stability of pathwise random periodic solutions for the stochastic lattice systems with delay. The convergence of the tempered complete quasi-solution (periodic solution) is also established when time delay approaches zero.

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Acknowledgments

This work was done while the first author was visiting Brigham Young University. He would like to acknowledge all the people there for the kind hospitality and thank China Scholarship Council for the support of the Visiting Scholar’s Program. This work is partially supported by National Natural Science Foundation of China (11331007,11201320) and Grants from NSF.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People‘s Republic of China

    Xiaohu Wang & Kening Lu

  2. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Kening Lu

  3. Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA

    Bixiang Wang

Authors
  1. Xiaohu Wang
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  2. Kening Lu
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  3. Bixiang Wang
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Correspondence to Kening Lu.

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Dedicated to Professor John Mallet-Paret on his 60th birthday.

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Wang, X., Lu, K. & Wang, B. Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise. J Dyn Diff Equat 28, 1309–1335 (2016). https://doi.org/10.1007/s10884-015-9448-8

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  • DOI: https://doi.org/10.1007/s10884-015-9448-8

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