Nilpotent Hopf bifurcations in coupled cell systems

SIAM Journal on Applied Dynamical Systems

Volumn 5, Issue 2, 2006, Pages 205-251

  Elmhirst, Toby ^a   Golubitsky, Martin ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b University of Houston   (United States)

Author keywords

Coupled cells; Hopf bifurcation; Nonsemisimple normal form

Indexed keywords

CELL SYSTEMS; COUPLED CELLS; COUPLED SYSTEMS; CRITICAL EIGENVALUES; GEOMETRIC MULTIPLICITIES; INVARIANT SUBSPACES; JACOBIANS; NILPOTENT; NONSEMISIMPLE NORMAL FORM; PERIODIC SOLUTIONS;

BIFURCATION (MATHEMATICS); NETWORK ARCHITECTURE;

HOPF BIFURCATION;

EID: 33745722793     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/050635559     Document Type: Article

References (10)

1. S. VAN GILS. M. KRUPA, AND W. LANGFORD, Hopf bifurcation with non-semisimple 1:1 resonance, Nonlinearity, 3 (1990), pp. 825-850.
2. M. GOLUBITSKY, M. NICOL, AND I. STEWART, Some curious phenomena in coupled cell networks, J. Nonlinear Sci., 14 (2004), pp. 119-236.
3. M. GOLUBITSKY AND D. G. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Vol. I, Appl. Math. Sci. 51, Springer-Verlag, New York, 1984.
4. M. GOLUBITSKY, I. N. STEWART, AND D. G. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Vol. II, Appl. Math. Sci. 69, Springer-Verlag, New York, 1988.
5. M. GOLUBITSKY, I. STEWART, AND A. TÖRÖ K, Patterns of synchrony in coupled cell networks with multiple arrows, SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 78-100.
6. M. LEITE, Homogeneous Three-Cell Networks, Ph.D. thesis, Department of Mathematics, University of Houston, Houston, TX, 2005.
7. M. LEITE AND M. GOLUBITSKY, Homogeneous three-cell networks, Networks, submitted.
8. N. S. NAMACHCHIVAYA, M. DOYLE, W. LANGFORD, AND N. EVANS, Normal form for generalized Hopf bifurcation with non-semisimple. 1:1 resonance, Z. Angew. Math. Phys., 45 (1994), pp. 312-335.
9. I. STEWART, M. GOLUBITSKY, AND M. PIVATO, Symmetry groupoids and patterns of synchrony in coupled cell networks, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 609-646.
10. A. VANDERBAUWHEDE, Hopf bifurcation at non-semisimple eigenvalues, in Multiparameter Bifurcation Theory, M. Golubitsky and J. Guckenheimer, eds., Contemp. Math. 56, AMS, Providence, RI, 1986, pp. 343-353.