메뉴 건너뛰기




Volumn 286, Issue 2, 1984, Pages 431-469

Stability of the travelling wave solution of the fitzhugh-nagumo system

Author keywords

Eigenvalue; Stability; Travelling wave; Winding number

Indexed keywords


EID: 84967743294     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1984-0760971-6     Document Type: Article
Times cited : (313)

References (23)
  • 1
    • 84967717397 scopus 로고    scopus 로고
    • Kolmogorov nonlinear diffusion equations
    • M. Bramson, Kolmogorov nonlinear diffusion equations, Mem. Amer. Math. Soc. (to appear).
    • Mem. Amer. Math. Soc.
    • Bramson, M.1
  • 3
    • 0010677632 scopus 로고
    • On travelling wave solutions of nonlinear diffusion equations, Dynamical Systems Theory and Applications
    • Springer-Verlag, Berlin
    • C. Conley, On travelling wave solutions of nonlinear diffusion equations, Dynamical Systems Theory and Applications (J. Moser, ed.), Lecture Notes in Physics, Vol. 38, Springer-Verlag, Berlin, 1975.
    • (1975) Lecture Notes in Physics , vol.38
    • Conley, C.1
  • 4
    • 0000329668 scopus 로고
    • An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model
    • C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, Indiana Univ. Math. J. 33 (1984), 319-343.
    • (1984) Indiana Univ. Math. J , vol.33 , pp. 319-343
    • Conley, C.1    Gardner, R.2
  • 6
    • 0001472248 scopus 로고
    • Nerve axon equations. I: Linear approximations
    • J. W. Evans, Nerve axon equations. I: Linear approximations, Indiana Univ. Math. J. 21 (1972), 877-955.
    • (1972) Indiana Univ. Math. J , vol.21 , pp. 877-955
    • Evans, J.W.1
  • 7
    • 0001472247 scopus 로고
    • Nerve axon equations. II: Stability at rest
    • J. W. Evans, Nerve axon equations. II: Stability at rest, Indiana Univ. Math. J. 22 (1972), 75-90.
    • (1972) Indiana Univ. Math. J , vol.22 , pp. 75-90
    • Evans, J.W.1
  • 9
    • 0016578299 scopus 로고
    • Nerve axon equations. IV: The stable and the unstable impulse
    • J. W. Evans, Nerve axon equations. IV: The stable and the unstable impulse, Indiana Univ. Math. J. 24 (1975), 1169-1190.
    • (1975) Indiana Univ. Math. J , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 10
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows, Indiana Univ
    • N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971), 193-226.
    • (1971) Math. J , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 11
    • 0017891591 scopus 로고
    • Temporal stability of solitary impulse solutions of a nerve equation
    • J. Feroe, Temporal stability of solitary impulse solutions of a nerve equation, Biophys. J. 21 (1978), 103-110.
    • (1978) Biophys. J , vol.21 , pp. 103-110
    • Feroe, J.1
  • 12
    • 0003299218 scopus 로고
    • Mathematical aspects of reacting and diffusing systems
    • Springer-Verlag, Berlin
    • P. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomath., Vol. 28, Springer-Verlag, Berlin, 1979.
    • (1979) Lecture Notes in Biomath. , vol.28
    • Fife, P.1
  • 13
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling front solutions
    • P. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361.
    • (1977) Arch. Rational Mech. Anal , vol.65 , pp. 335-361
    • Fife, P.1    McLeod, J.B.2
  • 14
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membranes
    • R. FitzHugh, Impulses and physiological states in theoretical models of nerve membranes, Biophys. J. 1 (1961), 445-466.
    • (1961) Biophys. J , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 15
    • 0346415941 scopus 로고
    • Existence and stability of travelling wave solutions of competition models: A degree theoretic approach
    • R. Gardner, Existence and stability of travelling wave solutions of competition models: a degree theoretic approach, J. Differential Equations 44 (1982), 343-364.
    • (1982) J. Differential Equations , vol.44 , pp. 343-364
    • Gardner, R.1
  • 16
    • 0039991189 scopus 로고
    • The existence of periodic travelling waves for singularly perturbed predator-prey equations via the Conley index
    • R. Gardner and J. Smoller, The existence of periodic travelling waves for singularly perturbed predator-prey equations via the Conley index, J. Differential Equations 47 (1983), 133-161.
    • (1983) J. Differential Equations , vol.47 , pp. 133-161
    • Gardner, R.1    Smoller, J.2
  • 17
    • 0001371673 scopus 로고
    • On the existence of homoclinic and periodic orbits for the FitzHugh-Nagumo equations
    • S. P. Hastings, On the existence of homoclinic and periodic orbits for the FitzHugh-Nagumo equations, Quart. J. Math. Oxford Ser. (2) 27 (1976), 123-134.
    • (1976) Quart. J. Math. Oxford Ser , vol.27 , Issue.2 , pp. 123-134
    • Hastings, S.P.1
  • 18
    • 0003304963 scopus 로고
    • The geometric theory of semilinear parabolic equations
    • Springer-Verlag, Berlin
    • D. Henry, The geometric theory of semilinear parabolic equations, Lecture Notes in Math., Vol. 840, Springer-Verlag, Berlin, 1981.
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 19
    • 0042337230 scopus 로고
    • The stability of travelling wave front solutions of a reaction-diffusion system, SIAM
    • G. Klaasen and W. Troy, The stability of travelling wave front solutions of a reaction-diffusion system, SIAM J. Appl. Math. 41 (1981), 145-167.
    • (1981) J. Appl. Math , vol.41 , pp. 145-167
    • Klaasen, G.1    Troy, W.2
  • 21
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axons
    • J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axons, Proc. IRL 50 (1960), 2061-2070.
    • (1960) Proc. IRL , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 22
    • 0002307123 scopus 로고
    • Qualitative theory of the FitzHugh-Nagumo equations
    • J. Rauch and J. Smoller, Qualitative theory of the FitzHugh-Nagumo equations, Adv. in Math. 27 (1978), 12-44.
    • (1978) Adv. in Math. , vol.27 , pp. 12-44
    • Rauch, J.1    Smoller, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.