非自治随机FitzHugh-Nagumo系统的随机一致指数吸引子
Random Uniform Exponential Attractor for Non-autonomous Stochastic FitzHugh-Nagumo System
本文首先给出了非自治随机动力系统的随机一致指数吸引子的概念及其存在性判据,其次证明了Rn上的带加法噪声和拟周期外力的FitzHugh—Nagumo系统的随机一致指数吸引子的存在性.
We first introduce the concept and the existence criterion of a random uniform exponential attractor for a non-autonomous random dynamical system. Then we prove the existence of a random uniform exponential attractor for FitzHugh-Nagumo system with additive noise and quasi-periodic external forces defined in Rn.
随机一致指数吸引子 / 非自治随机动力系统 / 随机FitzHugh&mdash / Nagumo系统 / 无界区域 {{custom_keyword}} /
random uniform exponential attractor / non-autonomous random dynamical system / stochastic FitzHugh-Nagumo system / unbounded domain {{custom_keyword}} /
[1] Abdallah A. Y., Uniform exponential attractors for first order non-autonomous lattice dynamical systems, J. Differential Equations, 2011, 251(6):1489-1504.
[2] Adams R. A., Fournier J. F., Sobolev Spaces, 2nd edition, Academic Press, New York, 2009.
[3] Adili A., Wang B., Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative noise, Discrete Contin. Dyn. Syst., 2013, Suppl:1-10.
[4] Adili A., Wang B., Random attractors for stochastic FitzHugh-Nagumo systems driven by deterministic non-autonomous forcing, Discrete Contin. Dyn. Syst. Ser. B, 2013, 18:643-666.
[5] Arnold L., Random Dynamical Systems, Springer-Verlag, New York, 2013.
[6] Carvalho A. N., Sonner S., Pullback exponential attractors for evolution processes in Banach spaces:theoretical results, Commun. Pure Appl. Anal., 2013, 12(6):3047-3071.
[7] Carvalho A. N., Sonner S., Pullback exponential attractors for evolution processes in Banach spaces:properties and applications, Commun. Pure Appl. Anal., 2014, 13(3):1141-1165.
[8] Caraballo T., Sonner S., Random pullback exponential attractors:General existence results for random dynamical systems in Banach spaces, Discrete Contin. Dyn. Syst., 2017, 37(12):6383-6403.
[9] Chepyzhov V. V., Vishik M. I., Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, RI, 2000.
[10] Chepyzhov V. V., Vishik M. I., Attractors of nonautonomous dynamical systems and their dimensions, J. Math. Pures Appl., 1994, 73(9):279-333.
[11] Cui H., Freitas M., Langa J. A., On random cocycle attractors with autonomous attraction universes, Discrete Contin. Dyn. Syst. Ser. B, 2017, 22(9):3379-3407.
[12] Cui H., Langa J. A., Uniform attractors for nonautonomous random dynamical systems, J. Differential Equations, 2017, 263(2):1225-1268.
[13] Czaja R., Efendiev M., Pullback exponential attractors for nonautonomous equations Part I:Semilinear parabolic problems, J. Math. Anal. Appl., 2011, 381(2):748-765.
[14] Du X., Guo B., The long time behavior for partly dissipative stochastic systems, J. Appl. Anal. Comput., 2011, 1(4):449-465.
[15] Eden A., Foias C., Nicolaenko B., et al., Exponential Attractors for Dissipative Evolution Equations, John Wiley & Sons, Ltd, Chichester, 1994.
[16] Efendiev M., Zelik S., Miranville A., Exponential attractors and finite-dimensional reduction for nonautonomous dynamical systems, Proc. Roy. Soc. Edinburgh Sect. A, 2005, 135(4):703-730.
[17] Fabrie P., Miranville A., Exponential attractors for nonautonomous first-order evolution equations, Discrete Contin. Dynam. Systems, 1998, 4(2):225-240.
[18] Fan X., Attractors for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise, Stoch. Anal. Appl., 2006, 24(4):767-793.
[19] FitzHugh R., Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1961, 1:445-466.
[20] Flandoli F., Schmalfuß B., Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise, Stochastics Stochastic Rep., 2007, 59(1-2):21-45.
国家自然科学基金资助项目(11871437)
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