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Volumn 21, Issue 7, 2008, Pages 1547-1578

Generic Hopf-Neǐmark-Sacker bifurcations in feed-forward systems

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EID: 44949236072     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/7/010     Document Type: Article
Times cited : (11)

References (33)
  • 3
    • 0001811172 scopus 로고
    • Toward a quasi-periodic bifurcation theory
    • Braaksma B L J, Broer H W and Huitema G B 1990 Toward a quasi-periodic bifurcation theory Mem. AMS vol 83 (Providence, RI: American Mathematical Society) pp 83-175
    • (1990) Mem. AMS , vol.83 , pp. 83-175
    • Braaksma, B.L.J.1    Broer, H.W.2    Huitema, G.B.3
  • 4
    • 0002761467 scopus 로고
    • Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case
    • Broer H W 1980 Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case Dynamical Systems and Turbulence (LNM) vol 898 (Berlin: Springer) pp 54-74
    • (1980) Dynamical Systems and Turbulence , vol.898 , pp. 54-74
    • Broer, H.W.1
  • 5
    • 0242371831 scopus 로고    scopus 로고
    • The geometry of resonance tongue: A singularity theory approach
    • Broer H W, Golubitsky M and Vegter G 2003 The geometry of resonance tongue: a singularity theory approach Nonlinearity 16 1511-38
    • (2003) Nonlinearity , vol.16 , Issue.4 , pp. 1511-1538
    • Broer, H.W.1    Golubitsky, M.2    Vegter, G.3
  • 7
    • 0142137606 scopus 로고    scopus 로고
    • Normal-internal resonances in quasi-periodically forces oscillators: A conservative approach
    • Broer H W, Hanßmann H, Jorba A, Villanueva J and Wagener F O O 2003 Normal-internal resonances in quasi-periodically forces oscillators: a conservative approach Nonlinearity 16 1751-91
    • (2003) Nonlinearity , vol.16 , Issue.5 , pp. 1751-1791
    • Broer, H.W.1    Hanßmann, H.2    Jorba, A.3    Villanueva, J.4    Wagener, F.O.O.5
  • 8
    • 44949249741 scopus 로고    scopus 로고
    • Broer H W, Holtman S J and Vegter G 2008 Recognition of the bifurcation type of resonance in mildly degenerate Hopf-Neîmark-Sacker families Technical Report Institute of Mathematics and Computer Science, University of Groningen URL: http://www.math.rug.nl/∼gert/documents/2008/ resonanceRecognitionBHV.pdf
    • (2008) Technical Report
    • Broer, H.W.1    Holtman, S.J.2    Vegter, G.3
  • 9
    • 16844380929 scopus 로고    scopus 로고
    • The parametrically forced pendulum: A case study in one-and-a-half degree of freedom
    • Broer H W, Hoveijn I, van Noort M, Simó C and Vegter G 2004 The parametrically forced pendulum: a case study in one-and-a-half degree of freedom J. Dyn Diff. Eqns 16 897-947
    • (2004) J. Dyn Diff. Eqns , vol.16 , Issue.4 , pp. 897-947
    • Broer, H.W.1    Hoveijn, I.2    Van Noort, M.3    Simó, C.4    Vegter, G.5
  • 10
    • 21844486186 scopus 로고
    • Geometrical aspects of stability theory for Hill's equations
    • Broer H W and Levi M 1995 Geometrical aspects of stability theory for Hill's equations Arch. Ration. Mech. Anal. 13 225-40
    • (1995) Arch. Ration. Mech. Anal. , vol.131 , Issue.3 , pp. 225-240
    • Broer, H.W.1    Levi, M.2
  • 11
    • 0242275980 scopus 로고    scopus 로고
    • Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation
    • Broer H W, Puig J and Simó C 2003 Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation Commun. Math. Phys. 241 467-503
    • (2003) Commun. Math. Phys. , vol.241 , Issue.2-3 , pp. 467-503
    • Broer, H.W.1    Puig, J.2    Simó, C.3
  • 12
    • 77957124197 scopus 로고    scopus 로고
    • KAM theory: Quasi-periodicity in dynamical systems
    • Broer H W and Sevryuk M B 2007 KAM theory: quasi-periodicity in dynamical systems Handbook of Dynamical Systems vol 3 ed H W Broer et al (Amsterdam: North-Holland) at press
    • (2007) Handbook of Dynamical Systems , vol.3
    • Broer, H.W.1    Sevryuk, M.B.2
  • 13
    • 0034692247 scopus 로고    scopus 로고
    • Resonance tongues in hill's equations: A geometric approach
    • Broer H W and Simó C 2000 Resonance tongues in hill's equations: a geometric approach J. Diff. Eqns 166 290-327
    • (2000) J. Diff. Eqns , vol.166 , Issue.2 , pp. 290-327
    • Broer, H.W.1    Simó, C.2
  • 14
    • 0006963160 scopus 로고    scopus 로고
    • Towards global models near homoclinic tangencies of dissipative diffeomorphisms
    • Broer H W, Simó C and Tatjer J-C 1998 Towards global models near homoclinic tangencies of dissipative diffeomorphisms Nonlinearity 11 667-770
    • (1998) Nonlinearity , vol.11 , Issue.3 , pp. 667-770
    • Broer, H.W.1    Simó, C.2    Tatjer, J.-C.3
  • 15
    • 0002208766 scopus 로고
    • Bifurcational aspects of parametric resonance
    • Broer H W and Vegter G 1992 Bifurcational aspects of parametric resonance Dynamics Reported (New Series) vol 1 (Berlin: Springer) pp 1-51
    • (1992) Dynamics Reported , vol.1 , pp. 1-51
    • Broer, H.W.1    Vegter, G.2
  • 16
    • 33646002283 scopus 로고    scopus 로고
    • Survey on dissipative Kam theory including quasi-periodic bifurcation theory based on lectures by Henk Broer
    • Ciocci M C, Litvak-Hinenzon A and Broer H W 2005 Survey on dissipative Kam theory including quasi-periodic bifurcation theory based on lectures by Henk Broer Geometric Mechanics and Symmetry: the Peyresq Lectures (LMS Lecture Notes Series) vol 306 ed J Montaldi and T Ratiu (Cambridge: Cambridge University Press) pp 303-55
    • (2005) Geometric Mechanics and Symmetry: The Peyresq Lectures , vol.306 , pp. 303-355
    • Ciocci, M.C.1    Litvak-Hinenzon, A.2    Broer, H.W.3
  • 17
    • 34547346692 scopus 로고    scopus 로고
    • Sensitive signal detection using a feed-forward oscillator network
    • Mc Cullen N J, Mullin T and Golubitsky M 2007 Sensitive signal detection using a feed-forward oscillator network Phys. Rev. Lett. 98 254101
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.25 , pp. 254101
    • Mc Cullen, N.J.1    Mullin, T.2    Golubitsky, M.3
  • 19
    • 33745722793 scopus 로고    scopus 로고
    • Nilpotent Hopf bifurcations in coupled cell networks
    • Elmhirst T and Golubitsky M 2006 Nilpotent Hopf bifurcations in coupled cell networks SIAM J. Appl. Dyn. Syst. 5 205-51
    • (2006) SIAM J. Appl. Dyn. Syst. , vol.5 , Issue.2 , pp. 205-251
    • Elmhirst, T.1    Golubitsky, M.2
  • 20
    • 0000523039 scopus 로고
    • Perturbation of a Hopf bifurcation by an external time-periodic forcing
    • Gambaudo J M 1985 Perturbation of a Hopf bifurcation by an external time-periodic forcing J. Diff. Eqns 57 172-99
    • (1985) J. Diff. Eqns , vol.57 , Issue.2 , pp. 172-199
    • Gambaudo, J.M.1
  • 21
    • 84868000314 scopus 로고    scopus 로고
    • Some curious phenomena in coupled cell networks
    • Golubitsky M, Nicol M and Stewart I 2004 Some curious phenomena in coupled cell networks J. Nonlin. Sci. 14 207-36
    • (2004) J. Nonlin. Sci. , vol.14 , Issue.2 , pp. 207-236
    • Golubitsky, M.1    Nicol, M.2    Stewart, I.3
  • 23
    • 11144319940 scopus 로고    scopus 로고
    • Patterns of synchrony in coupled cell networks with multiple arrows
    • Golubitsky M, Stewart I and Török A 2005 Patterns of synchrony in coupled cell networks with multiple arrows SIAM J. Appl. Dyn. Syst. 4 78-100
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , Issue.1 , pp. 78-100
    • Golubitsky, M.1    Stewart, I.2    Török, A.3
  • 25
    • 84980080650 scopus 로고
    • A mathematical example displaying features of turbulence
    • Hopf E 1948 A mathematical example displaying features of turbulence Commun. Appl. Math. 1 303-22
    • (1948) Commun. Appl. Math. , vol.1 , pp. 303-322
    • Hopf, E.1
  • 30
    • 0345792509 scopus 로고
    • Note concerning our paper on the nature of turbulence
    • Ruelle D and Takens F 1971 Note concerning our paper On the nature of turbulence Commun. Math. Phys. 23 343-44
    • (1971) Commun. Math. Phys. , vol.23 , pp. 343-344
    • Ruelle, D.1    Takens, F.2
  • 31
    • 34250451946 scopus 로고
    • On the nature of turbulence
    • Ruelle D and Takens F 1971 On the nature of turbulence Commun. Math. Phys. 20 167-92
    • (1971) Commun. Math. Phys. , vol.20 , Issue.3 , pp. 167-192
    • Ruelle, D.1    Takens, F.2
  • 32
    • 51649178043 scopus 로고
    • Singularities of vector fields
    • Takens F 1974 Singularities of vector fields Publ. Math. IHES 43 48-100
    • (1974) Publ. Math. IHES , vol.43 , Issue.1 , pp. 47-100
    • Takens, F.1


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