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Volumn 43, Issue 4, 2005, Pages 1407-1435

Numerical periodic normalization for codim 1 bifurcations of limit cycles

Author keywords

Bifurcations; Limit cycles; Normal forms

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; COMPUTATION THEORY; PROBLEM ORIENTED LANGUAGES;

EID: 33747182755     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040611306     Document Type: Article
Times cited : (34)

References (30)
  • 2
    • 0000319158 scopus 로고
    • Collocation at Gaussian points
    • C. DE BOOR AND B. SWARTZ, Collocation at Gaussian points, SIAM J. Numer. Anal., 10 (1973), pp. 582-606.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 582-606
    • De Boor, C.1    Swartz, B.2
  • 4
    • 0005049005 scopus 로고
    • Normal forms of bifurcating periodic orbits
    • Multiparameter Bifurcation Theory, AMS, Providence, RI
    • S.-N. CHOW AND D. WANG, Normal forms of bifurcating periodic orbits, in Multiparameter Bifurcation Theory, Contemp. Math. 56, AMS, Providence, RI, 1986, pp. 9-18.
    • (1986) Contemp. Math. , vol.56 , pp. 9-18
    • Chow, S.-N.1    Wang, D.2
  • 7
    • 0003327863 scopus 로고
    • Topics in Bifurcation Theory and Applications
    • World Scientific, River Edge, NJ
    • G. IOOSS AND M. ADELMEYER, Topics in Bifurcation Theory and Applications, Adv. Ser. Nonlinear Dynam. 3, World Scientific, River Edge, NJ, 1992.
    • (1992) Adv. Ser. Nonlinear Dynam. , vol.3
    • Iooss, G.1    Adelmeyer, M.2
  • 9
    • 0029640106 scopus 로고
    • Models of complex dynamics in nonlinear systems
    • R. GENESIO, A. TESI, AND F. VILLORESI, Models of complex dynamics in nonlinear systems, Systems Control Lett., 25 (1995), pp. 185-192.
    • (1995) Systems Control Lett. , vol.25 , pp. 185-192
    • Genesio, R.1    Tesi, A.2    Villoresi, F.3
  • 13
    • 0034967327 scopus 로고    scopus 로고
    • Computing periodic orbits and their bifurcations via automatic differentiation
    • J. GUCKENHEIMER AND B. MELOON, Computing periodic orbits and their bifurcations via automatic differentiation, SIAM J. SCi. Comput., 22 (2000), pp, 951-985.
    • (2000) SIAM J. SCi. Comput. , vol.22 , pp. 951-985
    • Guckenheimer, J.1    Meloon, B.2
  • 14
    • 27844523001 scopus 로고    scopus 로고
    • Numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues
    • YU. A. KUZNETSOV AND H. G. E. MEIJER, Numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues, SIAM J. Sci. Comput., 26 (2005), pp. 1932-1954.
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 1932-1954
    • Kuznetsov, Yu.A.1    Meijer, H.G.E.2
  • 15
    • 0002232810 scopus 로고
    • A simple global characterization for normal forms of singular vector fields
    • C. ELPHICK, E. TIRAPEGUI, M. E. BRACHET, P. H. COULLET, AND G. IOOSS, A simple global characterization for normal forms of singular vector fields, Phys. D, 32 (1987), pp. 95-127.
    • (1987) Phys. D , vol.32 , pp. 95-127
    • Elphick, C.1    Tirapegui, E.2    Brachet, M.E.3    Coullet, P.H.4    Iooss, G.5
  • 16
    • 0042941286 scopus 로고    scopus 로고
    • Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODEs
    • YU. A. KUZNETSOV, Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODEs, SIAM J. Numer. Anal., 36 (1999), pp. 1104-1124.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1104-1124
    • Kuznetsov, Yu.A.1
  • 17
    • 0001669344 scopus 로고
    • Normal form reduction for time-periodically driven differential equations
    • C. ELPHICK, G. IOOSS, AND E. TIRAPEGUI, Normal form reduction for time-periodically driven differential equations, Phys. Lett. A, 120 (1987), pp. 459-463.
    • (1987) Phys. Lett. A , vol.120 , pp. 459-463
    • Elphick, C.1    Iooss, G.2    Tirapegui, E.3
  • 18
    • 38249026752 scopus 로고
    • Global characterization of the normal form for a vector field near a closed orbit
    • G. IOOSS, Global characterization of the normal form for a vector field near a closed orbit, J. Differential Equations, 76 (1988), pp. 47-76.
    • (1988) J. Differential Equations , vol.76 , pp. 47-76
    • Iooss, G.1
  • 20
    • 8744230577 scopus 로고    scopus 로고
    • MATCONT; A MATLAB package for numerical bifurcation analysis of ODEs
    • A. DHOOGE, W. GOVAERTS, AND YU. A. KUZNETSOV, MATCONT; A MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans. Math. Software, 29 (2003), pp. 141-164.
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 141-164
    • Dhooge, A.1    Govaerts, W.2    Kuznetsov, Yu.A.3
  • 21
    • 0003344657 scopus 로고
    • Numerical solution of boundary value problems for ordinary differential equations
    • SIAM, Philadelphia
    • U. M. ASCHER, R. M. M. MATTHEIJ, AND R. D. RUSSELL, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Classics Appl. Math. 13, SIAM, Philadelphia, 1995.
    • (1995) Classics Appl. Math. , vol.13
    • Ascher, U.M.1    Mattheij, R.M.M.2    Russell, R.D.3
  • 22
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems. II. Bifurcation in infinite dimensions
    • E. DOEDEL, H. B. KELLER, AND J.-P. KERNÉVEZ, Numerical analysis and control of bifurcation problems. II. Bifurcation in infinite dimensions, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 1 (1991), pp. 745-772.
    • (1991) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.1 , pp. 745-772
    • Doedel, E.1    Keller, H.B.2    Kernévez, J.-P.3
  • 23
    • 2342460324 scopus 로고    scopus 로고
    • Computation of periodic solution bifurcations in ODEs using bordered systems
    • E. J. DOEDEL, W. GOVAERTS, AND YU. A. KUZNETSOV, Computation of periodic solution bifurcations in ODEs using bordered systems, SIAM J. Numer. Anal., 41 (2003), pp. 401-435.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 401-435
    • Doedel, E.J.1    Govaerts, W.2    Kuznetsov, Yu.A.3
  • 24
    • 0020876531 scopus 로고
    • Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with A → B → C reactions
    • E. J. DOEDEL AND R. P. HEINEMANN, Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with A → B → C reactions, Chem. Eng. Sci., 38 (1983), pp. 1493-1499.
    • (1983) Chem. Eng. Sci. , vol.38 , pp. 1493-1499
    • Doedel, E.J.1    Heinemann, R.P.2
  • 25
    • 0026866475 scopus 로고
    • Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
    • R. GENESIO AND A. TESI, Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems, Automatica, 28 (1992), pp. 531-548.
    • (1992) Automatica , vol.28 , pp. 531-548
    • Genesio, R.1    Tesi, A.2
  • 26
    • 0030235714 scopus 로고    scopus 로고
    • Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
    • A. TESI, E. H. ABED, R. GENESIO, AND H. O. WANG, Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics, Automatica, 32 (1996), pp. 1255-1271.
    • (1996) Automatica , vol.32 , pp. 1255-1271
    • Tesi, A.1    Abed, E.H.2    Genesio, R.3    Wang, H.O.4
  • 27
    • 0031678169 scopus 로고    scopus 로고
    • On the computation of characteristic multipliers for predicting limit cycle bifurcations
    • G. TORRINI, R. GENESIO, AND A. TESI, On the computation of characteristic multipliers for predicting limit cycle bifurcations, Chaos Solitons Fractals, 9 (1998), pp. 121-133.
    • (1998) Chaos Solitons Fractals , vol.9 , pp. 121-133
    • Torrini, G.1    Genesio, R.2    Tesi, A.3
  • 29
    • 0001444630 scopus 로고
    • The quasiperiodic route to chaos in a model of the peroxidase-oxidase reaction
    • C. G. STEINMETZ AND R. LARTER, The quasiperiodic route to chaos in a model of the peroxidase-oxidase reaction, J. Chem. Phys., 74 (1991), pp. 1388-1396.
    • (1991) J. Chem. Phys. , vol.74 , pp. 1388-1396
    • Steinmetz, C.G.1    Larter, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.