메뉴 건너뛰기




Volumn 12, Issue 4, 2000, Pages 733-806

Homoclinic twist bifurcation in a system of two coupled oscillators

Author keywords

Exponential dichotomy; Homoclinic twist bifurcation; 2

Indexed keywords


EID: 3042534951     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1009094505023     Document Type: Article
Times cited : (5)

References (17)
  • 3
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • [BC91] Benedicks, M., and Carleson, L. (1991). The dynamics of the Hénon map. Ann. Math. 2, 73-169.
    • (1991) Ann. Math. , vol.2 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 4
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homoclinic bifurcations
    • [CK94] Champneys, A. R., and Kuznetsov, Yu. A. (1994). Numerical detection and continuation of codimension-two homoclinic bifurcations. Int. J. Bifur. Chaos Appl. Sci. Eng. 4, 785-822.
    • (1994) Int. J. Bifur. Chaos Appl. Sci. Eng. , vol.4 , pp. 785-822
    • Champneys, A.R.1    Kuznetsov Yu., A.2
  • 5
    • 0003805267 scopus 로고
    • Lecture Notes in Maths, Springer, New York
    • [Cop78] Coppel, W. A. (1978). Dichotomies in Stability Theory, Lecture Notes in Maths, Vol. 629, Springer, New York.
    • (1978) Dichotomies in Stability Theory , vol.629
    • Coppel, W.A.1
  • 6
    • 0000851835 scopus 로고
    • Homoclinic twisting bifurcations and cusp horseshoe maps
    • [Den93] Deng, B. (1993). Homoclinic twisting bifurcations and cusp horseshoe maps. J. Dynam. Diff. Eq. 3, 417-467.
    • (1993) J. Dynam. Diff. Eq. , vol.3 , pp. 417-467
    • Deng, B.1
  • 8
    • 2042442839 scopus 로고
    • Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study
    • [FD93] Friedman, M., and Doedel, E. (1994). Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study. J. Dynam. Diff. Eq. 5, 37-51.
    • (1994) J. Dynam. Diff. Eq. , vol.5 , pp. 37-51
    • Friedman, M.1    Doedel, E.2
  • 9
    • 0001559874 scopus 로고
    • Cusp horseshoes in the unfoldings of the inclination flip bifurcation points
    • [HKK94] Homburg, A. J., Kokubu, H., and Krupa, M. (1994). Cusp horseshoes in the unfoldings of the inclination flip bifurcation points. Ergod. Theor. Dynam. Syst. 4, 667-639.
    • (1994) Ergod. Theor. Dynam. Syst. , vol.4 , pp. 667-1639
    • Homburg, A.J.1    Kokubu, H.2    Krupa, M.3
  • 10
    • 0001580295 scopus 로고
    • Supplement to homoclinic doubling bifurcation in vector fields, dynamical systems
    • Lewowicz, J., Bamon, R., Labarca, J., and Palis, J. (eds.), Longman Sci Tech., Harlow
    • [KKO93] Kisaka, M., Kokubu, H., and Oka, H. (1993). Supplement to homoclinic doubling bifurcation in vector fields, dynamical systems. In Lewowicz, J., Bamon, R., Labarca, J., and Palis, J. (eds.), Pitman Res. Notes Math. Ser., Vol. 285, Longman Sci Tech., Harlow, pp. 92-116.
    • (1993) Pitman Res. Notes Math. Ser. , vol.285 , pp. 92-116
    • Kisaka, M.1    Kokubu, H.2    Oka, H.3
  • 11
    • 84972438215 scopus 로고
    • Using Melnikov's method to solve silnikov's problems
    • [Lin90] Lin, X. B. (1990). Using Melnikov's method to solve silnikov's problems. Proc. Roy. Soc. Edingburgh A 116, 295-325.
    • (1990) Proc. Roy. Soc. Edingburgh A , vol.116 , pp. 295-325
    • Lin, X.B.1
  • 12
    • 45449122562 scopus 로고
    • Symmetry increasing bifurcations of chaotic attractors
    • [PG88] Chossat, P., and Golubitsky, M. (1988). Symmetry increasing bifurcations of chaotic attractors. Physica D 32, 423-436.
    • (1988) Physica D , vol.32 , pp. 423-436
    • Chossat, P.1    Golubitsky, M.2
  • 14
    • 0001215210 scopus 로고
    • On the generation of periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type
    • [Shi68] Shilnikov, L. P. (1968). On the generation of periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Mat. USSR sb. 6, 427-437.
    • (1968) Mat. USSR Sb. , vol.6 , pp. 427-437
    • Shilnikov, L.P.1
  • 15
    • 0012104323 scopus 로고
    • Bifurcation of degenerate homoclinics
    • [Van92] Vanderbauwhede, A. (1992). Bifurcation of degenerate homoclinics. Results Math. 21.
    • (1992) Results Math. , pp. 21
    • Vanderbauwhede, A.1
  • 17
    • 0002422398 scopus 로고
    • Branching of double pulse solutions from single pulse solutions in nerve axon equations
    • [Yan87] Yanagida, E. (1987). Branching of double pulse solutions from single pulse solutions in nerve axon equations. J. Diff. Eq. 66, 243-262.
    • (1987) J. Diff. Eq. , vol.66 , pp. 243-262
    • Yanagida, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.