Stochastic Stability of FitzHugh-Nagumo Systems Perturbed by Gaussian White Noise
-
摘要: 在Gauss噪声扰动下FitzHugh-Nagumo系统的随机稳定性是该文的研究目的.通过研究随机FitzHugh-Nagumo系统的动力学行为, 证明其存在唯一的、具有指数混合速度的不变测度.最后, 考察当噪声趋于0时不变测度的渐近行为.
-
关键词:
- 随机稳定性 /
- FitzHugh-Nagumo系统 /
- 不变测度 /
- Gauss白噪声
Abstract: Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise was studied.The dynamics of stochastic FitzHugh-Nagumo systems was studied first,which is essential in establishing the existence and uniqueness of their invariant measures,which mix exponentially.Then,asymptotic behavior of invariant measures when the size of noise gets to zero was investigated. -
[1] Has’minskii R Z.Stochastic Stability of Differential Equations[M].Dordrecht: Kluwer Academic Publishers, 1981. [2] Kifer Y.Random Perturbations of Dynamical Systems[M]. Boston: Birkhuser, 1988. [3] Baladi V.Positive Transfer Operators and Decay of Correlations[M]. Advanced Series in Nonlinear Dynamics. Vol 16. New Jersey: World Scientific Publishing Co, Inc, 2000. [4] Blank M.Discreteness and Continuity in Problems of Chaotic Dynamics[M].Transl Math Monographs. Vol 116. Providence,RI, United States: American Mathematical Society, 1997. [5] Viana M.Stochastic Dynamics of Deterministic Systems[M].Brazil: Col Bras de Matemti ̄ca, 1997. [6] Babin A, Vishik M.Attractors of Evolution Equations[M]. Amsterdam: North-Holland, 1992. [7] Martine M. Finite-dimensional attractors associated with partly dissipative reaction-diffusion systems[J].SIAM J Math Anal,1989, 20(4): 816-844. doi: 10.1137/0520057 [8] Rodriguez-Bernal A, Wang B. Attractor for partly dissipative reaction diffusion systems in Rn[J].J Math Anal Appl, 2000, 252(2): 790-803. doi: 10.1006/jmaa.2000.7122 [9] Robinson J.Infinite-Dimensional Dynamical Systems, an Introduction to Dissipative Parabolic PDEs and Theory of Global Attractors[M]. Cambridge: Cambridge University Press, 2001. [10] Teman R.Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York: Springer-Verlag, 1988. [11] 杨美华, 钟承奎. 无界域上部分耗散系统解的全局存在性和唯一性[J].兰州大学学报(自然科学版), 2006, 42(5): 130-136.(YANG Mei-hua, ZHONG Cheng-kui. The existence and uniqueness of the solutions for partly dissipative reaction diffusion systems in Rn[J].J Lanzhou University(Natural Sciences), 2006, 42(5): 130-136.(in Chinese)) [12] Magalha~es P, Coayla-Tern E.Weak solution for stochastic FitzHugh-Nagumo equations[J].Stochastic Analysis and Applications, 2003, 21(2): 443-463. doi: 10.1081/SAP-120019294 [13] Huang J, Shen W. Global attractors for partly dissipative random/stochastic reaction diffusion systems[J].International Journal of Evolution Equations, 2009, 4(4): 383-412. [14] Da Prato G, Zabczyk J. Ergodicity for Infinite Dimensional Systems[M]. Cambridge:Cambridge University Press, 1996. [15] Da Prato G, Zabczyk J. Convergence to equilibrium for classical and quantum spin systems[J].Probability Theory and Ralat Fields, 1995, 103(4): 529-552. doi: 10.1007/BF01246338 [16] Peszat S, Zabczyk J.Stochastic Partial Differential Equations With Lévy Noise[M]. Cambridge:Cambridge University Press, 2007. [17] Vleck E, Wang B. Attractors for lattice FitzHugh-Nagumo systems[J].Physica D, 2005, 212(3/4): 317-336. doi: 10.1016/j.physd.2005.10.006
点击查看大图
计量
- 文章访问数: 1271
- HTML全文浏览量: 86
- PDF下载量: 751
- 被引次数: 0