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Volumn 467, Issue 2132, 2011, Pages 2404-2421

Canards and curvature: The 'smallness of 3' in slow-fast dynamics

Author keywords

Canard; Curvature; Inflection; Slow fast dynamics

Indexed keywords

AEROSPACE ENGINEERING; CIRCUIT OSCILLATIONS; DYNAMICAL SYSTEMS; EXPLOSIONS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES;

EID: 80051722401     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2011.0053     Document Type: Conference Paper
Times cited : (35)

References (24)
  • 2
    • 0023743550 scopus 로고
    • Bifurcations and instabilities in the Greitzer model for compressor system surge
    • Brøns, M. 1988 Bifurcations and instabilities in the Greitzer model for compressor system surge. Math. Eng. Ind. 2, 51-63.
    • (1988) Math. Eng. Ind. , vol.2 , pp. 51-63
    • Brøns, M.1
  • 3
    • 0028011298 scopus 로고
    • Asymptotic analysis of canards in the EOE equations and the role of the inflection line
    • Brøns, M. & Bar-Eli, K. 1994 Asymptotic analysis of canards in the EOE equations and the role of the inflection line. Proc. R. Soc. Lond. A 445, 305-322. (doi:10.1098/rspa.1994.0063) (Pubitemid 285070)
    • (1994) Proceedings - Royal Society of London, A , vol.445 , Issue.1924 , pp. 305-322
    • Brons, M.1    Bar-Eli, K.2
  • 5
    • 0002294440 scopus 로고
    • The canard unchained or how fast/slow dynamical systems bifurcate
    • doi:10.1007/BF03024127
    • Diener, M. 1984 The canard unchained or how fast/slow dynamical systems bifurcate. Math. Intelligencer 6, 38-49. (doi:10.1007/BF03024127)
    • (1984) Math. Intelligencer , vol.6 , pp. 38-49
    • Diener, M.1
  • 8
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • doi:10.1512/iumj.1971.21.21017
    • Fenichel, N. 1972 Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193-226. (doi:10.1512/iumj.1971.21.21017)
    • (1972) Indiana Univ. Math. J. , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 9
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • doi:10.1016/0022-0396(79)90152-9
    • Fenichel, N. 1979 Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 53-98. (doi:10.1016/0022-0396(79) 90152-9)
    • (1979) J. Differ. Equ. , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 10
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • doi:10.1016/S0006-3495(61)86902-6
    • FitzHugh, R. 1961 Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466. (doi:10.1016/S0006-3495(61)86902-6)
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 11
    • 85077337128 scopus 로고    scopus 로고
    • World Scientific Series on Nonlinear Science, Series A. Singapore: World Scientific
    • Ginoux, J.-M. 2009 Differential geometry applied to dynamical systems, vol. 66. World Scientific Series on Nonlinear Science, Series A. Singapore: World Scientific.
    • (2009) Differential Geometry Applied to Dynamical Systems , vol.66
    • Ginoux, J.-M.1
  • 12
    • 33745305351 scopus 로고    scopus 로고
    • Differential geometry and mechanics: Applications to chaotic dynamical systems
    • DOI 10.1142/S0218127406015192, PII S0218127406015192
    • Ginoux, J.-M. & Rossetto, B. 2006a Differential geometry and mechanics: applications to chaotic dynamical systems. Int. J. Bifurcat. Chaos 16, 887-910. (doi:10.1142/S0218127406015192) (Pubitemid 43936688)
    • (2006) International Journal of Bifurcation and Chaos , vol.16 , Issue.4 , pp. 887-910
    • Ginoux, J.-M.1    Rossetto, B.2
  • 14
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first-order differential equations
    • doi:10.1098/rspb.1984.0024
    • Hindmarsh, J. L. & Rose, R. M. 1984 A model of neuronal bursting using three coupled first-order differential equations. Proc. R. Soc. Lond. B 221, 87-102. (doi:10.1098/rspb.1984.0024)
    • (1984) Proc. R. Soc. Lond. B , vol.221 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 15
    • 0003706768 scopus 로고
    • Lecture Notes in Mathematics. Berlin, Germany: Springer
    • Hirsch, M. W., Pugh, C. C. & Shub, M. 1977 Invariant manifolds, vol. 583. Lecture Notes in Mathematics. Berlin, Germany: Springer.
    • (1977) Invariant Manifolds , vol.583
    • Hirsch, M.W.1    Pugh, C.C.2    Shub, M.3
  • 16
    • 0035839416 scopus 로고    scopus 로고
    • Relaxation oscillation and canard explosion
    • DOI 10.1006/jdeq.2000.3929, PII S0022039600939299
    • Krupa, M. & Szmolyan, P. 2001 Relaxation oscillation and canard explosion. J. Differ. Equ. 174, 312-368. (doi:10.1006/jdeq.2000.3929) (Pubitemid 33378729)
    • (2001) Journal of Differential Equations , vol.174 , Issue.2 , pp. 312-368
    • Krupa, M.1    Szmolyan, P.2
  • 17
    • 55949135112 scopus 로고    scopus 로고
    • Mixed-mode oscillations in three time-scale systems: A prototypical example
    • doi:10.1137/070688912
    • Krupa, M., Popovíc, N. & Kopell, N. 2008 Mixed-mode oscillations in three time-scale systems: a prototypical example. SIAM J. Appl. Dyn. Syst. 7, 361-402. (doi:10.1137/070688912)
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 361-402
    • Krupa, M.1    Popovíc, N.2    Kopell, N.3
  • 19
    • 31544467353 scopus 로고    scopus 로고
    • Canards for a reduction of the Hodgkin-Huxley equations
    • DOI 10.1007/s00285-005-0347-1
    • Moehlis, J. 2006 Canards for a reduction of the Hodgkin-Huxley equations. J. Math. Biol. 52, 141-153. (doi:10.1007/s00285-005-0347-1) (Pubitemid 43155411)
    • (2006) Journal of Mathematical Biology , vol.52 , Issue.2 , pp. 141-153
    • Moehlis, J.1
  • 20
    • 0041362530 scopus 로고
    • False bifurcations in chemical systems: Canards
    • doi:10.1098/rsta.1991.0123
    • Peng, B., Gaspar, V. & Showalter, K. 1991 False bifurcations in chemical systems: canards. Phil. Trans. R. Soc. Lond. A 337, 275-289. (doi:10.1098/rsta.1991.0123)
    • (1991) Phil. Trans. R. Soc. Lond. A , vol.337 , pp. 275-289
    • Peng, B.1    Gaspar, V.2    Showalter, K.3
  • 21
    • 65249132884 scopus 로고    scopus 로고
    • Mixed-mode dynamics and the canard phenomenon: Towards a classification
    • doi:10.1088/1742-6596/138/1/012020
    • Popovíc, N. 2008 Mixed-mode dynamics and the canard phenomenon: towards a classification. J. Phys. Conf. Ser. 138, 012 020. (doi:10.1088/1742- 6596/138/1/012020)
    • (2008) J. Phys. Conf. Ser. , vol.138 , pp. 012-020
    • Popovíc, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.