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Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains

Abstract

The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system. We prove that the system has a pullback random attractor that is compact in Hs(ℝn) × L2(ℝn) and attracts all tempered random sets of L2(ℝn) × L2(ℝn) in the topology of Hs(ℝn) × L2(ℝn) with s ∈ (0, 1). By the idea of positive and negative truncations, spectral decomposition in bounded domains, and tail estimates, we achieved the desired results.

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Acknowledgements

The authors are grateful to the reviewers for many helpful comments. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11771444, 11871138), the Yue Qi Young Scholar Project, China University of Mining and Technology (Beijing), China Scholarship Council (CSC), the Funding of V.C. & V.R. Key Lab of Sichuan Province, the Funding of Young Backbone Teacher in Henan Province, and Henan Overseas Expertise Introduction Center for Discipline Innovation.

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Correspondence to Ji Shu.

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Guo, C., Chen, Y., Shu, J. et al. Dynamical behaviors of non-autonomous fractional FitzHugh-Nagumo system driven by additive noise in unbounded domains. Front. Math. China 16, 59–93 (2021). https://doi.org/10.1007/s11464-021-0896-7

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Keywords

  • Fractional stochastic FitzHugh-Nagumo system
  • random attractor
  • asymptotic compactness

MSC2020

  • 60H15
  • 35B05
  • 48F23