메뉴 건너뛰기




Volumn 11, Issue 4, 2010, Pages 3091-3105

Limit dynamics for the stochastic FitzHugh-Nagumo system

Author keywords

Random attractor; Random dynamical system; Stochastic FitzHughNagumo system; Tightness

Indexed keywords

ASYMPTOTIC BEHAVIORS; FITZHUGH-NAGUMO SYSTEMS; FUNCTIONAL SPACES; ORIGINAL SYSTEMS; RANDOM ATTRACTORS; RANDOM DYNAMICAL SYSTEM; SEMI-GROUP; TIGHTNESS; UPPER SEMI-CONTINUITY;

EID: 77955775947     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.11.004     Document Type: Article
Times cited : (13)

References (29)
  • 1
    • 0019582693 scopus 로고
    • Some threshold results for models of myelinated nerves
    • J. Bell Some threshold results for models of myelinated nerves Math. Biosci. 54 1981 181 190
    • (1981) Math. Biosci. , vol.54 , pp. 181-190
    • Bell, J.1
  • 2
    • 53349102813 scopus 로고
    • Impulse and physiological states in theoretical models of nerve membrane
    • R. FitzHugh Impulse and physiological states in theoretical models of nerve membrane Biophys. J. 1 1961 445 466
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 4
    • 0035831562 scopus 로고    scopus 로고
    • Spiking behavior in a noise-driven system combining oscillatory and excitatory properties
    • V.A. Makarov, V.I. Nekorkin, and M.G. Velarde Spiking behavior in a noise-driven system combining oscillatory and excitatory properties Phys. Rev. Lett. 86 2001 3431 3434
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 3431-3434
    • Makarov, V.A.1    Nekorkin, V.I.2    Velarde, M.G.3
  • 5
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • J. Nagumo, S. Arimoto, and S. Yosimzawa An active pulse transmission line simulating nerve axon Proc. J. R. E. 50 1964 2061 2070
    • (1964) Proc. J. R. E. , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yosimzawa, S.3
  • 6
    • 0000997882 scopus 로고
    • The existence of infinite many travelling front and back waves in the FitzHughNagumo equations
    • B. Deng The existence of infinite many travelling front and back waves in the FitzHughNagumo equations SIAM J. Math. Anal. 22 1991 1631 1650
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1631-1650
    • Deng, B.1
  • 7
    • 84967743294 scopus 로고
    • Stability of the travelling waves solution of the FitzHughNagumo system
    • C. Jones Stability of the travelling waves solution of the FitzHughNagumo system Trans. Amer. Math. Soc. 286 1984 431 469
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.1
  • 8
    • 0000247056 scopus 로고
    • Finite-dimensional attractors associated with partly dissipative reaction-diffusion systems
    • M. Marion Finite-dimensional attractors associated with partly dissipative reaction-diffusion systems SIAM J. Math. Anal. 20 1989 816 844
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 816-844
    • Marion, M.1
  • 9
    • 0002077212 scopus 로고    scopus 로고
    • Existence of inertial manifold for partly dissipative reaction-diffusion systems in higher space dimensions
    • Z. Shao Existence of inertial manifold for partly dissipative reaction-diffusion systems in higher space dimensions J. Differential Equations 144 1998 1 43
    • (1998) J. Differential Equations , vol.144 , pp. 1-43
    • Shao, Z.1
  • 11
    • 33751162151 scopus 로고    scopus 로고
    • Stochastic resonance in an extended FitzHughNagumo system: The role of selective coupling
    • J. Tessonea, and H.S. Wiob Stochastic resonance in an extended FitzHughNagumo system: The role of selective coupling Physica A 374 1 2007 46 54
    • (2007) Physica A , vol.374 , Issue.1 , pp. 46-54
    • Tessonea, J.1    Wiob, H.S.2
  • 12
    • 36048975698 scopus 로고    scopus 로고
    • Limit dynamics for stochastic wave equations
    • Y. Lv, and W. Wang Limit dynamics for stochastic wave equations J. Differential Equations 244 2008 1 23
    • (2008) J. Differential Equations , vol.244 , pp. 1-23
    • Lv, Y.1    Wang, W.2
  • 14
    • 18544364615 scopus 로고    scopus 로고
    • Some recent progress in multiscale modeling
    • Multiscale Modeling and Simulation Springer Berlin
    • W. E, X. Li, and E. Vanden-Eijnden Some recent progress in multiscale modeling Multiscale Modeling and Simulation Lecture Notes in Comput. Sci. Eng. vol. 39 2004 Springer Berlin 3 21
    • (2004) Lecture Notes in Comput. Sci. Eng. , vol.39 , pp. 3-21
    • Li, X.1    Vanden-Eijnden, E.2
  • 15
    • 76549085573 scopus 로고    scopus 로고
    • Probability and Partial Differential Equations in Modern Applied Mathematics
    • Springer-Verlag New York
    • E. Waymire, J. Duan, Probability and Partial Differential Equations in Modern Applied Mathematics IMA vol. 140 2005 Springer-Verlag New York
    • (2005) IMA , vol.140
    • Waymire, E.1    Duan, J.2
  • 19
    • 0346961357 scopus 로고    scopus 로고
    • Invariant manifolds for stochastic partial differential equations
    • DOI 10.1214/aop/1068646380
    • J. Duan, K. Lu, and B. Schmalfuß Invariant manifolds for stochastic partial differential equations Ann. Probab. 31 4 2003 2109 2135 (Pubitemid 37537585)
    • (2003) Annals of Probability , vol.31 , Issue.4 , pp. 2109-2135
    • Duan, J.1    Lu, K.2    Schmalfuss, B.3
  • 20
    • 0003263856 scopus 로고
    • Smooth Ergodic theory of Random Dynamical Systems
    • Springer-Verlag Berlin
    • P.D. Liu, and M. Qian Smooth Ergodic theory of Random Dynamical Systems Lect. Notes in Math vol. 1606 1995 Springer-Verlag Berlin
    • (1995) Lect. Notes in Math , vol.1606
    • Liu, P.D.1    Qian, M.2
  • 22
    • 0038270631 scopus 로고    scopus 로고
    • Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
    • S. Cerrai Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term Probab. Theory Relat. Fields 125 2003 271 304
    • (2003) Probab. Theory Relat. Fields , vol.125 , pp. 271-304
    • Cerrai, S.1
  • 26
    • 33750360109 scopus 로고    scopus 로고
    • Global attractors of nonautonomous dissipative dynamical systems
    • World Scientific
    • D. Cheban Global attractors of nonautonomous dissipative dynamical systems Interdisciplinary Mathematical Sciences, vol. 1 2004 World Scientific
    • (2004) Interdisciplinary Mathematical Sciences, Vol. 1
    • Cheban, D.1
  • 28
    • 0037059105 scopus 로고    scopus 로고
    • Stability of random attractors under perturbation and approximation
    • J.C. Robinson Stability of random attractors under perturbation and approximation J. Differential Equations 186 2002 652 669
    • (2002) J. Differential Equations , vol.186 , pp. 652-669
    • Robinson, J.C.1
  • 29
    • 0001642365 scopus 로고    scopus 로고
    • Upper semicontinuity of attractors for small random perturbations of dynamical systems
    • T. Caraballo, J.A. Langa, and J.C. Robinson Upper semicontinuity of attractors for small random perturbations of dynamical systems Comm. Partial Differential Equations 23 1998 1557 1581
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 1557-1581
    • Caraballo, T.1    Langa, J.A.2    Robinson, J.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.