메뉴 건너뛰기




Volumn 11, Issue 12, 2001, Pages 3059-3083

Chaotic attractors in one-dimension generated by a singular Shilnikov orbit

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035655545     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401004005     Document Type: Article
Times cited : (3)

References (28)
  • 2
    • 0000465402 scopus 로고
    • Singular perturbation of relaxed periodic orbits
    • Bonet, C. [1987] "Singular perturbation of relaxed periodic orbits,"J. D. E. 66, 301-339.
    • (1987) J. D. E. , vol.66 , pp. 301-339
    • Bonet, C.1
  • 3
    • 0026899565 scopus 로고
    • The genesis of Chua's circuit
    • Chua, L. O. [1992] "The genesis of Chua's circuit," AEÜ 46, 250-257.
    • (1992) AEÜ , vol.46 , pp. 250-257
    • Chua, L.O.1
  • 4
    • 0001477835 scopus 로고
    • Transition to stochasticity for a class of forced oscillators
    • Coullet, P., Tresser, C. & Arnéodo, A. [1979] "Transition to stochasticity for a class of forced oscillators," Phys. Lett. A72, 268-270.
    • (1979) Phys. Lett. , vol.A72 , pp. 268-270
    • Coullet, P.1    Tresser, C.2    Arnéodo, A.3
  • 6
    • 0001630378 scopus 로고
    • Šil'nikov's homoclinic-saddle-focus theorem
    • Deng, B. [1993a] "Šil'nikov's homoclinic-saddle-focus theorem," J. D. E. 102, 305-329.
    • (1993) J. D. E. , vol.102 , pp. 305-329
    • Deng, B.1
  • 7
    • 0000851835 scopus 로고
    • Homoclinic twisting bifurcations and cusp horseshoe maps
    • Deng, B. [1993b] "Homoclinic twisting bifurcations and cusp horseshoe maps," J. Dyn. Diff. Eqs. 5, 417-467.
    • (1993) J. Dyn. Diff. Eqs. , vol.5 , pp. 417-467
    • Deng, B.1
  • 8
    • 21844517849 scopus 로고
    • Construction homoclinic orbits and chaotic attractors
    • Deng, B. [1994] "Construction homoclinic orbits and chaotic attractors," Int. J. Bifurcation and Chaos 4, 823-841.
    • (1994) Int. J. Bifurcation and Chaos , vol.4 , pp. 823-841
    • Deng, B.1
  • 9
    • 21844510580 scopus 로고
    • Constructing Lorenz type attractors through singular perturbations
    • Deng, B. [1995] "Constructing Lorenz type attractors through singular perturbations," Int. J. Bifurcation and Chaos 5, 1633-1642.
    • (1995) Int. J. Bifurcation and Chaos , vol.5 , pp. 1633-1642
    • Deng, B.1
  • 10
    • 58149362431 scopus 로고
    • The subshift dynamics for the attractor near an orbit homoclinic to a Hopf equilibrium
    • Deng, B. & Sakamoto, K. [1995] "The subshift dynamics for the attractor near an orbit homoclinic to a Hopf equilibrium," J. D. E. 119, 1-23.
    • (1995) J. D. E. , vol.119 , pp. 1-23
    • Deng, B.1    Sakamoto, K.2
  • 11
    • 0030093599 scopus 로고    scopus 로고
    • Spiral-plus-saddle attractors and elementary mechanisms for chaos generation
    • Deng, B. [1996a] "Spiral-plus-saddle attractors and elementary mechanisms for chaos generation," Int. J. Bifurcation and Chaos 6, 513-527.
    • (1996) Int. J. Bifurcation and Chaos , vol.6 , pp. 513-527
    • Deng, B.1
  • 12
    • 0000553690 scopus 로고    scopus 로고
    • Folding at the genesis of chaos
    • Lakshmikantham, V. (Walter de Gruyter, Berlin/NY)
    • Deng, B. [1996b] "Folding at the genesis of chaos," Proc. First World Congress of Nonliniear Analysts' 92, ed. Lakshmikantham, V. (Walter de Gruyter, Berlin/NY), 3765-3777.
    • (1996) Proc. First World Congress of Nonliniear Analysts' 92, Ed. , pp. 3765-3777
    • Deng, B.1
  • 13
    • 0032603032 scopus 로고    scopus 로고
    • Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells
    • Deng, B. [1999] "Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells," J. Math. Biol. 38, 21-78.
    • (1999) J. Math. Biol. , vol.38 , pp. 21-78
    • Deng, B.1
  • 15
    • 0001477332 scopus 로고
    • Double impulse solutions in nerve axon equations
    • Evans, J. W., Fenichel, N. & Feroe, J. A. [1982] "Double impulse solutions in nerve axon equations," SIAM J. Appl. Math. 42, 219-234.
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 219-234
    • Evans, J.W.1    Fenichel, N.2    Feroe, J.A.3
  • 16
    • 11844295560 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel, N. [1979] "Geometric singular perturbation theory for ordinary differential equations," J. D. E. 73, 513-527.
    • (1979) J. D. E. , vol.73 , pp. 513-527
    • Fenichel, N.1
  • 18
    • 0000967056 scopus 로고
    • Single and multiple impulse waves for the FitzHugh-Nagumo equations
    • Hastings, S. P. [1982] "Single and multiple impulse waves for the FitzHugh-Nagumo equations," SIAM J. Appl. Math. 42, 247-260.
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 247-260
    • Hastings, S.P.1
  • 22
    • 24844441872 scopus 로고
    • Chaotic behavior in simple reaction systems
    • Rössler, O. E. [1976] "Chaotic behavior in simple reaction systems," Z. Naturforsch A31, 259-264.
    • (1976) Z. Naturforsch , vol.A31 , pp. 259-264
    • Rössler, O.E.1
  • 23
    • 84985456277 scopus 로고
    • Continuous chaos - Four prototype equations
    • eds. Gurd, O. & Rössler, O. E., Annals of The New York Academy of Science
    • Rössler, O. E. [1979] "Continuous chaos - four prototype equations," in Bifurcation Theory and Applications in Scientific Disciplines, eds. Gurd, O. & Rössler, O. E., Annals of The New York Academy of Science, Vol. 316, pp. 376-392.
    • (1979) Bifurcation Theory and Applications in Scientific Disciplines , vol.316 , pp. 376-392
    • Rössler, O.E.1
  • 24
    • 0001234956 scopus 로고
    • A case of the existence of a denumerable set of periodic motions
    • Šil'nikov, L. P. [1965] "A case of the existence of a denumerable set of periodic motions," Sov. Math. Dokl. 6, 163-166.
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 163-166
    • Šil'Nikov, L.P.1
  • 25
    • 0002997859 scopus 로고
    • The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve
    • Šil'nikov, L. P. [1967] "The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve," Sov. Math. Dokl. 8, 102-106.
    • (1967) Sov. Math. Dokl. , vol.8 , pp. 102-106
    • Šil'Nikov, L.P.1
  • 26
    • 84956230541 scopus 로고
    • A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of a saddle-focus type
    • Šil'nikov, L. P. [1970] "A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of a saddle-focus type," Math. USSR-Sb 10, 91-102.
    • (1970) Math. USSR-Sb , vol.10 , pp. 91-102
    • Šil'Nikov, L.P.1
  • 28
    • 0000615851 scopus 로고
    • About some theorems by L. P. Silnikov
    • Tresser, C. [1984] "About some theorems by L. P. Silnikov," Ann. Inst. H. Poincaré 40, 440-461.
    • (1984) Ann. Inst. H. Poincaré , vol.40 , pp. 440-461
    • Tresser, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.