메뉴 건너뛰기




Volumn 253, Issue 8, 2012, Pages 2527-2557

Global generic dynamics close to symmetry

Author keywords

Bykov cycles; Heteroclinic networks; Shilnikov's homoclinic cycles; Symmetry breaking

Indexed keywords


EID: 84864292151     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2012.06.009     Document Type: Article
Times cited : (25)

References (43)
  • 1
    • 0001495825 scopus 로고
    • On the entropy of a flow
    • (in Russian)
    • Abramov L. On the entropy of a flow. Dokl. Akad. Nauk SSSR 1959, 128:873-875. (in Russian).
    • (1959) Dokl. Akad. Nauk SSSR , vol.128 , pp. 873-875
    • Abramov, L.1
  • 2
    • 11844284112 scopus 로고    scopus 로고
    • Vector Fields with heteroclinic networks
    • PhD thesis, Departamento de Matemática Aplicada, Faculdade de Ciências da Universidade do Porto
    • M. Aguiar, Vector Fields with heteroclinic networks, PhD thesis, Departamento de Matemática Aplicada, Faculdade de Ciências da Universidade do Porto, 2003.
    • (2003)
    • Aguiar, M.1
  • 5
    • 77949590053 scopus 로고    scopus 로고
    • Swicthing near a heteroclinic network of rotating nodes
    • Aguiar M., Labouriau I.S., Rodrigues A. Swicthing near a heteroclinic network of rotating nodes. Dyn. Syst. 2010, 25(1):75-95.
    • (2010) Dyn. Syst. , vol.25 , Issue.1 , pp. 75-95
    • Aguiar, M.1    Labouriau, I.S.2    Rodrigues, A.3
  • 8
    • 0001218019 scopus 로고
    • Convection in a rotating layer: A simple case of turbulence
    • Busse F.H., Heikes K.E. Convection in a rotating layer: A simple case of turbulence. Science 1980, 208(4440):173-175.
    • (1980) Science , vol.208 , Issue.4440 , pp. 173-175
    • Busse, F.H.1    Heikes, K.E.2
  • 9
    • 0242312061 scopus 로고    scopus 로고
    • Orbit Structure in a Neighbourhood of a Separatrix Cycle Containing Two Saddle-Foci
    • Bykov V.V. Orbit Structure in a Neighbourhood of a Separatrix Cycle Containing Two Saddle-Foci. Amer. Math. Soc. Transl. 2000, vol. 200. pp. 87-97.
    • (2000) Amer. Math. Soc. Transl. , vol.200 , pp. 87-97
    • Bykov, V.V.1
  • 10
    • 34047181411 scopus 로고    scopus 로고
    • Origin of bursting through homoclinic spike adding in a neuron model
    • Channell P., Cymbalyuk G., Shilnikov A. Origin of bursting through homoclinic spike adding in a neuron model. Phys. Rev. Lett. 2007, 98:134101-134105.
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 134101-134105
    • Channell, P.1    Cymbalyuk, G.2    Shilnikov, A.3
  • 11
    • 0242276338 scopus 로고    scopus 로고
    • Parameter dependence of homoclinic solutions in a single long Josepson junction
    • van den Berg J.B., van Gils S.A., Visser T.P.P. Parameter dependence of homoclinic solutions in a single long Josepson junction. Nonlinearity 2003, 2(16):707-717.
    • (2003) Nonlinearity , vol.2 , Issue.16 , pp. 707-717
    • van den Berg, J.B.1    van Gils, S.A.2    Visser, T.P.P.3
  • 12
    • 55849142205 scopus 로고    scopus 로고
    • Existence of a reversible T-point heteroclinic cycle in a piecewise linear version of the Michelson system
    • Carmona V., Sánchez F.F., Teruel A.E. Existence of a reversible T-point heteroclinic cycle in a piecewise linear version of the Michelson system. SIAM J. Appl. Dyn. Syst. 2008, 1032-1048.
    • (2008) SIAM J. Appl. Dyn. Syst. , pp. 1032-1048
    • Carmona, V.1    Sánchez, F.F.2    Teruel, A.E.3
  • 13
    • 84864309301 scopus 로고    scopus 로고
    • Forced reflectional symmetry breaking of an O(2)-symmetric homoclinic cycle
    • Chossat P. Forced reflectional symmetry breaking of an O(2)-symmetric homoclinic cycle. Nonlinearity 1996, 70(2):297-310.
    • (1996) Nonlinearity , vol.70 , Issue.2 , pp. 297-310
    • Chossat, P.1
  • 14
    • 10944235170 scopus 로고    scopus 로고
    • Comportamiento dinámico y de bifurcationes en algunas conexiones globales de equilíbrio en sistemas tridimensionales
    • PhD thesis, University of Sevilla
    • F. Fernández-Sanchez, Comportamiento dinámico y de bifurcationes en algunas conexiones globales de equilíbrio en sistemas tridimensionales, PhD thesis, University of Sevilla, 2002.
    • (2002)
    • Fernández-Sanchez, F.1
  • 17
    • 0007646794 scopus 로고
    • Generation of a countable set of homoclinic flows through bifurcation
    • Gaspard P. Generation of a countable set of homoclinic flows through bifurcation. Phys. Lett. A 1983, 97(1-2):1-4.
    • (1983) Phys. Lett. A , vol.97 , Issue.1-2 , pp. 1-4
    • Gaspard, P.1
  • 19
    • 0021437639 scopus 로고
    • Local and global behavior near homoclinic orbits
    • Glendinning P., Sparrow C. Local and global behavior near homoclinic orbits. J. Stat. Phys. 1984, 35:645-696.
    • (1984) J. Stat. Phys. , vol.35 , pp. 645-696
    • Glendinning, P.1    Sparrow, C.2
  • 20
    • 34250127220 scopus 로고
    • T-points: A codimension two heteroclinic bifurcation
    • Glendinning P., Sparrow C. T-points: A codimension two heteroclinic bifurcation. J. Stat. Phys. 1986, 43(3-4):479-488.
    • (1986) J. Stat. Phys. , vol.43 , Issue.3-4 , pp. 479-488
    • Glendinning, P.1    Sparrow, C.2
  • 22
    • 1842449685 scopus 로고    scopus 로고
    • Determination of generalized horseshoe map inducing all links
    • Hirasawa M., Kin E. Determination of generalized horseshoe map inducing all links. Topology Appl. 2004, 139(1-3):261-277.
    • (2004) Topology Appl. , vol.139 , Issue.1-3 , pp. 261-277
    • Hirasawa, M.1    Kin, E.2
  • 23
    • 77958158886 scopus 로고    scopus 로고
    • Switching homoclinic networks
    • Homburg A.J., Knobloch J. Switching homoclinic networks. Dyn. Syst. 2010, 25(3):351-358.
    • (2010) Dyn. Syst. , vol.25 , Issue.3 , pp. 351-358
    • Homburg, A.J.1    Knobloch, J.2
  • 24
    • 14044267496 scopus 로고    scopus 로고
    • Accumulations of T-points in a model for solitary pulses in an excitable reaction-diffusion medium
    • Homburg A.J., Natiello M.A. Accumulations of T-points in a model for solitary pulses in an excitable reaction-diffusion medium. Phys. D 2005, 201(3-4):212-229.
    • (2005) Phys. D , vol.201 , Issue.3-4 , pp. 212-229
    • Homburg, A.J.1    Natiello, M.A.2
  • 27
    • 0034413688 scopus 로고    scopus 로고
    • The third power of the Smale horseshoe induces all link types
    • Kin E. The third power of the Smale horseshoe induces all link types. J. Knot Theory Ramifications 2000, 9(7):939-953.
    • (2000) J. Knot Theory Ramifications , vol.9 , Issue.7 , pp. 939-953
    • Kin, E.1
  • 28
    • 41549148229 scopus 로고    scopus 로고
    • The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
    • Kirk V., Rucklidge A.M. The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit. Dyn. Syst. 2008, 23(1):41-83.
    • (2008) Dyn. Syst. , vol.23 , Issue.1 , pp. 41-83
    • Kirk, V.1    Rucklidge, A.M.2
  • 29
    • 84864303026 scopus 로고    scopus 로고
    • Nonreversible homoclinic snaking, preprint
    • J. Knobloch, T. Riez, M. Vielits, Nonreversible homoclinic snaking, preprint, 2010.
    • (2010)
    • Knobloch, J.1    Riez, T.2    Vielits, M.3
  • 30
    • 84974489205 scopus 로고
    • Asymptotic stability of heteroclinic cycles in systems with symmetry
    • Krupa M., Melbourne I. Asymptotic stability of heteroclinic cycles in systems with symmetry. Ergodic Theory Dynam. Systems 1995, 15:121-147.
    • (1995) Ergodic Theory Dynam. Systems , vol.15 , pp. 121-147
    • Krupa, M.1    Melbourne, I.2
  • 32
    • 0002077676 scopus 로고
    • Intermittency as a codimension three phenomenon
    • Melbourne I. Intermittency as a codimension three phenomenon. J. Dyn. Stab. Syst. 1989, 1:347-367.
    • (1989) J. Dyn. Stab. Syst. , vol.1 , pp. 347-367
    • Melbourne, I.1
  • 34
    • 0242344635 scopus 로고
    • Abundance of strange attractors
    • Mora L., Viana M. Abundance of strange attractors. Acta Math. 1993, 171:1-71.
    • (1993) Acta Math. , vol.171 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 35
    • 0037768575 scopus 로고    scopus 로고
    • 1-normal forms for hyperbolic vector fields
    • 1-normal forms for hyperbolic vector fields. C. R. Acad. Sci. Paris Ser. I 2003, 336(9):709-712.
    • (2003) C. R. Acad. Sci. Paris Ser. I , vol.336 , Issue.9 , pp. 709-712
    • Ren, Z.1    Yang, J.2
  • 37
    • 0009325376 scopus 로고
    • Linearization of a system of differential equations in the neighbourhood of a singular point
    • Samovol V.S. Linearization of a system of differential equations in the neighbourhood of a singular point. Sov. Math. Dokl. 1972, 13:1255-1959.
    • (1972) Sov. Math. Dokl. , vol.13 , pp. 1255-1959
    • Samovol, V.S.1
  • 38
    • 0001234956 scopus 로고
    • A case of the existence of a countable number of periodic motions
    • Shilnikov L.P. A case of the existence of a countable number of periodic motions. Sov. Math. Dokl. 1965, 6:163-166.
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 163-166
    • Shilnikov, L.P.1
  • 42
    • 0026401577 scopus 로고
    • Coexistence of the chaos and the periodic solutions in planar fluids flows
    • (English version)
    • Xiao-feng Y., Rui-hai G. Coexistence of the chaos and the periodic solutions in planar fluids flows. Applied Mathematics and Mechanics 1991, 12(12):1135-1142. (English version).
    • (1991) Applied Mathematics and Mechanics , vol.12 , Issue.12 , pp. 1135-1142
    • Xiao-feng, Y.1    Rui-hai, G.2
  • 43
    • 0002223697 scopus 로고
    • Period-doubling cascade of attractors: A prerequisite for horseshoes
    • Yorke J.A., Alligood K.T. Period-doubling cascade of attractors: A prerequisite for horseshoes. Comm. Math. Phys. 1985, 101:305-321.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 305-321
    • Yorke, J.A.1    Alligood, K.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.