메뉴 건너뛰기




Volumn 3, Issue 4, 2002, Pages 515-541

Singular perturbation of N-front travelling waves in the Fitzhugh-Nagumo equations

Author keywords

Fitzhugh Nagumo equations; Geometric theory of singular perturbations; N front travelling waves

Indexed keywords


EID: 0036887506     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(01)00046-3     Document Type: Article
Times cited : (39)

References (23)
  • 1
    • 23044522889 scopus 로고    scopus 로고
    • Invariant foliations near normally hyperbolic invariant manifolds for semiflows
    • P.W. Bates, K.N. Lu, C.C. Zeng, Invariant foliations near normally hyperbolic invariant manifolds for semiflows, Trans. Amer. Math. Soc. 352 (2000) 4641-4676.
    • (2000) Trans. Amer. Math. Soc , vol.352 , pp. 4641-4676
    • Bates, P.W.1    Lu, K.N.2    Zeng, C.C.3
  • 2
    • 0010683728 scopus 로고    scopus 로고
    • The uniform bifurcation of n-front travelling waves in the singularly perturbed Fitzhugh-Nagumo equations
    • Ph.D. Thesis, University of Nebraska-Lincoln
    • D.C. Bell, The uniform bifurcation of n-front travelling waves in the singularly perturbed Fitzhugh-Nagumo equations, Ph.D. Thesis, University of Nebraska-Lincoln, 1999.
    • (1999)
    • Bell, D.C.1
  • 3
    • 0033542204 scopus 로고    scopus 로고
    • k-inclination theorems for singularly perturbed equations
    • k-inclination theorems for singularly perturbed equations, J. Differential Equations 155 (1999) 133-152.
    • (1999) J. Differential Equations , vol.155 , pp. 133-152
    • Brunovsky, P.1
  • 4
    • 0010863128 scopus 로고
    • A geometric approach to singular perturbation problems with applications to nerve impulse equations
    • G.A. Carpenter, A geometric approach to singular perturbation problems with applications to nerve impulse equations, J. Differential Equations 23 (1977) 335-367.
    • (1977) J. Differential Equations , vol.23 , pp. 335-367
    • Carpenter, G.A.1
  • 5
    • 84972533582 scopus 로고
    • Bifurcation of a homoclinic orbit with a saddle-node equilibrium
    • S.-N. Chow, X.-B. Lin, Bifurcation of a homoclinic orbit with a saddle-node equilibrium, Differential Integral Equations 3 (1990) 435-466.
    • (1990) Differential Integral Equations , vol.3 , pp. 435-466
    • Chow, S.-N.1    Lin, X.-B.2
  • 6
    • 0000025015 scopus 로고
    • Homoclinic bifurcations with nonhyperbolic equilibria
    • B. Deng, Homoclinic bifurcations with nonhyperbolic equilibria, SIAM. J. Math. Anal. 21 (1990) 693-719.
    • (1990) SIAM. J. Math. Anal , vol.21 , pp. 693-719
    • Deng, B.1
  • 7
    • 0000775150 scopus 로고
    • The bifurcations of countable connections from a twisted heteroclinic loop
    • B. Deng, The bifurcations of countable connections from a twisted heteroclinic loop, SIAM J. Math. Anal. 22 (1991) 653-679.
    • (1991) SIAM J. Math. Anal , vol.22 , pp. 653-679
    • Deng, B.1
  • 8
    • 0000997882 scopus 로고
    • The existence of infinitely many travelling front and back waves in the Fitzhugh-Nagumo equations
    • B. Deng, The existence of infinitely many travelling front and back waves in the Fitzhugh-Nagumo equations, SIAM J. Math. Anal. 22 (1991) 1631-1650.
    • (1991) SIAM J. Math. Anal , vol.22 , pp. 1631-1650
    • Deng, B.1
  • 9
    • 0016578299 scopus 로고
    • Nerve axon equations, IV: The stable and unstable impulse
    • J. Evans, Nerve axon equations, IV: the stable and unstable impulse, Indiana Univ. Math. J. 24 (1975) 1169-1190.
    • (1975) Indiana Univ. Math. J , vol.24 , pp. 1169-1190
    • Evans, J.1
  • 10
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations 31 (1979) 53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 11
    • 0002721581 scopus 로고
    • Mathematical models of excitation and propagation in nerve
    • H.P. Schwan (Ed.), McGraw-Hill, New York
    • R. Fitzhugh, Mathematical models of excitation and propagation in nerve, in: H.P. Schwan (Ed.), Biological Engineering, McGraw-Hill, New York, 1969, pp. 1-85.
    • (1969) Biological Engineering , pp. 1-85
    • Fitzhugh, R.1
  • 12
    • 0000967056 scopus 로고
    • Single and multiple pulse waves for the Fitzhugh-Nagumo equations
    • S. Hastings, Single and multiple pulse waves for the Fitzhugh-Nagumo equations, SIAM J. Appl. Math. 42 (1982) 247-260.
    • (1982) SIAM J. Appl. Math , vol.42 , pp. 247-260
    • Hastings, S.1
  • 13
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952) 500-544.
    • (1952) J. Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 14
    • 84967743294 scopus 로고
    • Stability of the travelling pulse of the Fitzhugh-Nagumo system
    • C.K.R.T. Jones, Stability of the travelling pulse of the Fitzhugh-Nagumo system, Trans. AMS 286 (1984) 31-469.
    • (1984) Trans. AMS , vol.286 , pp. 31-469
    • Jones, C.K.R.T.1
  • 15
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • 1609, Springer, Berlin
    • C.K.R.T. Jones, Geometric singular perturbation theory, Lecture Notes in Mathematics, Vol. 1609, Springer, Berlin, 1995, pp. 44-118.
    • (1995) Lecture Notes in Mathematics , pp. 44-118
    • Jones, C.K.R.T.1
  • 16
    • 0000263519 scopus 로고
    • Construction of the Fitzhugh-Nagumo pulse using differential forms
    • Patterns and Dynamics in Reactive Media, Springer, New York
    • C.K.R.T. Jones, N. Kopell, Construction of the Fitzhugh-Nagumo pulse using differential forms, in: Patterns and Dynamics in Reactive Media, IMA Math. Appl. Vol. 37, Springer, New York, 1991, pp. 101-115.
    • (1991) IMA Math. Appl , vol.37 , pp. 101-115
    • Jones, C.K.R.T.1    Kopell, N.2
  • 17
    • 38249016389 scopus 로고
    • Heteroclinic and homoclinic bifurcations in bistable reaction diffusion system
    • H. Kokubu, Y. Nishiura, H. Oka, Heteroclinic and homoclinic bifurcations in bistable reaction diffusion system, J. Differential Equations 86 (1990) 260-341.
    • (1990) J. Differential Equations , vol.86 , pp. 260-341
    • Kokubu, H.1    Nishiura, Y.2    Oka, H.3
  • 18
    • 0003858468 scopus 로고
    • Existence of homoclinic travelling wave solutions to the Fitzhugh-Nagumo Equations
    • Ph.D. Thesis, Northeastern University
    • R. Langer, Existence of homoclinic travelling wave solutions to the Fitzhugh-Nagumo Equations, Ph.D. Thesis, Northeastern University, 1980.
    • (1980)
    • Langer, R.1
  • 19
    • 3042538112 scopus 로고    scopus 로고
    • Stability of the traveling N-front (N-back) wave solutions of the Fitzhugh-Nagumo equations
    • S. Nii, Stability of the traveling N-front (N-back) wave solutions of the Fitzhugh-Nagumo equations, SIAM J. Math. Anal. 28 (1997) 1094-1112.
    • (1997) SIAM J. Math. Anal , vol.28 , pp. 1094-1112
    • Nii, S.1
  • 20
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • K.J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations 55 (1984) 225-265.
    • (1984) J. Differential Equations , vol.55 , pp. 225-265
    • Palmer, K.J.1
  • 21
    • 0010646864 scopus 로고
    • Integation and propagation of neuroelectric signals
    • S.A. Levin (Ed.), The Mathematical Association of America, Providence RI
    • J. Rinzel, Integation and propagation of neuroelectric signals, in: S.A. Levin (Ed.), Studies in Mathematical Biology, The Mathematical Association of America, Providence RI, 1978, pp. 1-66.
    • (1978) Studies in Mathematical Biology , pp. 1-66
    • Rinzel, J.1
  • 22
    • 0020191444 scopus 로고
    • Propagation phenomena in a bistable reaction-diffusion system
    • J. Rinzel, D. Terman, Propagation phenomena in a bistable reaction-diffusion system, SIAM J. Appl. Math. 42 (1982) 1111-1137.
    • (1982) SIAM J. Appl. Math , vol.42 , pp. 1111-1137
    • Rinzel, J.1    Terman, D.2
  • 23
    • 0032338132 scopus 로고    scopus 로고
    • Stablitie of N-fronts bifurcating from a twisted heteroclinic loop and an application to the Fitzhugh-Nagumo equation
    • B. Sandstede, Stablitie of N-fronts bifurcating from a twisted heteroclinic loop and an application to the Fitzhugh-Nagumo equation, SIAM J. Math. Anal. 29 (1998) 183-207.
    • (1998) SIAM J. Math. Anal , vol.29 , pp. 183-207
    • Sandstede, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.