REGULARITY OF PULLBACK ATTRACTORS AND RANDOM EQUILIBRIUM FOR NON-AUTONOMOUS STOCHASTIC FITZHUGH-NAGUMO SYSTEM ON UNBOUNDED DOMAINS

Wenqiang Zhao; Anhui Gu

doi:10.11948/2017079

2017 Volume 7 Issue 4

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Wenqiang Zhao, Anhui Gu. REGULARITY OF PULLBACK ATTRACTORS AND RANDOM EQUILIBRIUM FOR NON-AUTONOMOUS STOCHASTIC FITZHUGH-NAGUMO SYSTEM ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1285-1311. doi: 10.11948/2017079

Citation:

Wenqiang Zhao, Anhui Gu. REGULARITY OF PULLBACK ATTRACTORS AND RANDOM EQUILIBRIUM FOR NON-AUTONOMOUS STOCHASTIC FITZHUGH-NAGUMO SYSTEM ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1285-1311. doi: 10.11948/2017079

REGULARITY OF PULLBACK ATTRACTORS AND RANDOM EQUILIBRIUM FOR NON-AUTONOMOUS STOCHASTIC FITZHUGH-NAGUMO SYSTEM ON UNBOUNDED DOMAINS

Wenqiang Zhao¹,
Anhui Gu²

1 School of Mathematics and Statistics, Chongqing Technology and Business University, 400067 Chongqing, China;
2 School of Mathematics and statistics, Southwest University, 400715 Chongqing, China

Fund Project:

Abstract

Abstract

This paper is concerned with the stochastic Fitzhugh-Nagumo system with non-autonomous terms as well as Wiener type multiplicative noises. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, the existences and upper semi-continuity of pullback attractors are proved for the generated random cocycle in L^l(R^N)×L²(R^N) for any l ∈ (2,p]. The asymptotic compactness of the first component of the system in L^p(R^N) is proved by a new asymptotic a priori estimate technique, by which the plus or minus sign of the nonlinearity at large values is not required. Moreover, the condition on the existence of the unique random fixed point is obtained, in which case the influence of physical parameters on the attractors is analysed.
- Random dynamical system /
- non-autonomous FitzHugh-Nagumo system /
- upper semi-continuity /
- pullback attractor /
- random fixed point
MSC: 60H15;35B40;35B41

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References

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