摘要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. | | 服务 | | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | 加入引用管理器 | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | E-mail Alert | ![](http://www.actamath.com/Jwk_sxxb_cn/images/arrow.jpg) | RSS | 收稿日期: 2019-11-04 | | 基金资助:国家自然科学基金资助项目(11871437)
| 通讯作者:周胜凡,E-mail:zhoushengfan@yahoo.comE-mail: zhoushengfan@yahoo.com |
[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.
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[1] | 黄心中. 单位圆到水平条形无界区域的调和拟共形映照[J]. Acta Mathematica Sinica, English Series, 2014, 57(5): 875-880. | [2] | 陈光淦;蒲志林;魏赟赟. 无界区域R~1上的KDV型方程的指数吸引子[J]. Acta Mathematica Sinica, English Series, 2004, 47(3): 441-448. | [3] | 黄毅生;周育英. 无界区域上含p-Laplacian的共振问题[J]. Acta Mathematica Sinica, English Series, 2002, 45(5): 841-846. | [4] | 赵春山;李开泰. 无界区域上非自治Navier-Stokes方程的一致吸引子及其维数估计[J]. Acta Mathematica Sinica, English Series, 2000, 43(1): 33-42. | [5] | 黄少云;王耀东. 无界区域上非稳定井流的自由边界问题[J]. Acta Mathematica Sinica, English Series, 1983, 26(3): 354-377. | [6] | 应隆安;韩厚德. 关于无界区域和非齐次问题的无限元法[J]. Acta Mathematica Sinica, English Series, 1980, 23(1): 118-127. | [7] | 沈爕昌. 用函数系{z~(τn)log~jz}来逼近复平面上的函数[J]. Acta Mathematica Sinica, English Series, 1964, 14(3): 406-414. | [8] | 沈燮昌. 论函数序列{f(λ_nΖ)}的完备性[J]. Acta Mathematica Sinica, English Series, 1964, 14(1): 103-118. | [9] | 沈燮昌. 关于函数系{z~(τn)log~jz}在复数平面上的区域中的完备性問題[J]. Acta Mathematica Sinica, English Series, 1963, 13(3): 405-418. |
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