Random attractors for stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions

Ranran Liu; Hui Liu; Jie Xin; Ranran Liu; Hui Liu; Jie Xin

doi:10.3934/math.2021175

AIMS Mathematics

2021, Volume 6, Issue 3: 2900-2911. doi: 10.3934/math.2021175

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Research article

Random attractors for stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P. R. China
2.
School of Mathematics and Statistics, Ludong University, Yantai, Shandong, 264025, P. R. China
3.
College of Information Science and Engineering, Shandong Agricultural University, Tai An, Shandong, 271018, P. R. China

Received: 07 October 2020 Accepted: 29 December 2020 Published: 07 January 2021
MSC : 37H05, 60G22, 60H15

We study the dynamical behavior of the solutions of stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions with Hurst parameter $ H\in(\frac{1}{2}, 1) $. And then we prove that the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.
- stochastic discrete long wave-short wave resonance equation,
- random attractor,
- fractional Brownian motion
Citation: Ranran Liu, Hui Liu, Jie Xin. Random attractors for stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions[J]. AIMS Mathematics, 2021, 6(3): 2900-2911. doi: 10.3934/math.2021175

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Abstract

We study the dynamical behavior of the solutions of stochastic discrete long wave-short wave resonance equations driven by fractional Brownian motions with Hurst parameter $ H\in(\frac{1}{2}, 1) $. And then we prove that the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor.

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