메뉴 건너뛰기




Volumn 175, Issue 2, 2006, Pages 932-968

A Maple program for computing a terms of a center manifold, and element of bifurcations for a class of retarded functional differential equations with Hopf singularity

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); COMPUTER SOFTWARE; LYAPUNOV METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 33645887211     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.08.013     Document Type: Article
Times cited : (13)

References (21)
  • 1
    • 0031220762 scopus 로고    scopus 로고
    • Approximation scheme of a system manifold for functional differential equations
    • Ait Babram M., Arino O., and Hbid M.L. Approximation scheme of a system manifold for functional differential equations. J. Math. Anal. Appl. 213 (1997) 554-572
    • (1997) J. Math. Anal. Appl. , vol.213 , pp. 554-572
    • Ait Babram, M.1    Arino, O.2    Hbid, M.L.3
  • 2
    • 0035877501 scopus 로고    scopus 로고
    • Computational scheme of a center manifold for neutral functional differential equations
    • Ait Babram M., Arino O., and Hbid M.L. Computational scheme of a center manifold for neutral functional differential equations. J. Math. Anal. Appl. 258 (2001) 396-414
    • (2001) J. Math. Anal. Appl. , vol.258 , pp. 396-414
    • Ait Babram, M.1    Arino, O.2    Hbid, M.L.3
  • 3
    • 0003369834 scopus 로고
    • Poincaré procedure for an ordinary differential system perturbed by a functional term
    • Arino O., and Hbid M.L. Poincaré procedure for an ordinary differential system perturbed by a functional term. J. Different. Eqs. Dynam. Syst. 2 2 (1994) 113-120
    • (1994) J. Different. Eqs. Dynam. Syst. , vol.2 , Issue.2 , pp. 113-120
    • Arino, O.1    Hbid, M.L.2
  • 4
    • 0042787523 scopus 로고
    • Quasi-invariant manifolds stability and generalized Hopf bifurcation
    • Bernfeld S.R., Negrini P., and Salvadori L. Quasi-invariant manifolds stability and generalized Hopf bifurcation. Ann. Math. Pura Appl. 4 (1982) 105-119
    • (1982) Ann. Math. Pura Appl. , vol.4 , pp. 105-119
    • Bernfeld, S.R.1    Negrini, P.2    Salvadori, L.3
  • 5
    • 85025413675 scopus 로고
    • Generalized Hopf bifurcation and h-asymptotic stability
    • Bernfeld S.R., and Salvadori L. Generalized Hopf bifurcation and h-asymptotic stability. J. Nonlinear Anal. TMA 4 6 (1980) 1091-1107
    • (1980) J. Nonlinear Anal. TMA , vol.4 , Issue.6 , pp. 1091-1107
    • Bernfeld, S.R.1    Salvadori, L.2
  • 8
    • 0024037022 scopus 로고
    • Normal forms for nonlinear vector fields-Part I: Theory and algorithm
    • Chua L.O., and Cocubu H. Normal forms for nonlinear vector fields-Part I: Theory and algorithm. IEEE Trans. Circ. Syst. 35 (1988) 836-880
    • (1988) IEEE Trans. Circ. Syst. , vol.35 , pp. 836-880
    • Chua, L.O.1    Cocubu, H.2
  • 9
    • 33645848921 scopus 로고    scopus 로고
    • O. Diekmann, S.A. Van Gils, The center manifold for delay equations in light sun stars, in: M. Roberts, I.N. Stewart (Eds.), Singularity Theory and its Application, Warwick, 1989, Part II, Springer LNM 1464, 1991, pp. 122-141.
  • 10
    • 0000840164 scopus 로고
    • Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
    • Faria T., and Magalhàes L.T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Different. Eqs. 122 (1995) 181-200
    • (1995) J. Different. Eqs. , vol.122 , pp. 181-200
    • Faria, T.1    Magalhàes, L.T.2
  • 11
    • 0000840165 scopus 로고
    • Normal forms for retarded functional differential equations and applications to Bogdanov-Takens bifurcation
    • Faria T., and Magalhàes L.T. Normal forms for retarded functional differential equations and applications to Bogdanov-Takens bifurcation. J. Different. Eqs. 122 (1995) 201-224
    • (1995) J. Different. Eqs. , vol.122 , pp. 201-224
    • Faria, T.1    Magalhàes, L.T.2
  • 13
    • 0039439327 scopus 로고
    • Springer-Verlag, NY
    • Henry D. Geometric Theory of Semi-linear Parabolic Equations. Lect. Notes in Math. 840 (1981), Springer-Verlag, NY
    • (1981) Lect. Notes in Math. 840
    • Henry, D.1
  • 14
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • Rabinowitz P. (Ed), Academic Press, New York
    • Keller H. Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Rabinowitz P. (Ed). Applications of Bifurcation Theory (1977), Academic Press, New York 359-384
    • (1977) Applications of Bifurcation Theory , pp. 359-384
    • Keller, H.1
  • 15
    • 0005828897 scopus 로고    scopus 로고
    • Stability and bifurcation in delay differential equations with two delays
    • Li X., Ruan S., and Wei J. Stability and bifurcation in delay differential equations with two delays. J. Math. Anal. Appl. 236 (1999) 254-280
    • (1999) J. Math. Anal. Appl. , vol.236 , pp. 254-280
    • Li, X.1    Ruan, S.2    Wei, J.3
  • 16
    • 0002953859 scopus 로고
    • Attractivity and Hopf bifurcation
    • Negrini P., and Salvadori L. Attractivity and Hopf bifurcation. Nonlinear Anal. 3 (1979) 87-100
    • (1979) Nonlinear Anal. , vol.3 , pp. 87-100
    • Negrini, P.1    Salvadori, L.2
  • 17
    • 0043288570 scopus 로고    scopus 로고
    • Hopf bifurcation via the Poincaré procedure in differential equations with two delays
    • Ouifki R., Hbid M.L., and Arino O. Hopf bifurcation via the Poincaré procedure in differential equations with two delays. Commun. Pure Appl. Anal. 2 (2003) 147-158
    • (2003) Commun. Pure Appl. Anal. , vol.2 , pp. 147-158
    • Ouifki, R.1    Hbid, M.L.2    Arino, O.3
  • 18
    • 0035507108 scopus 로고    scopus 로고
    • Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response
    • Ruan S., and Xiao D. Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response. J. Different. Eqs. 176 (2001) 494-510
    • (2001) J. Different. Eqs. , vol.176 , pp. 494-510
    • Ruan, S.1    Xiao, D.2
  • 19
    • 18344377026 scopus 로고    scopus 로고
    • Delayed stochastic differential model for quiet standing
    • Yao W., Yu P., and Essex C. Delayed stochastic differential model for quiet standing. Phys. Rev. E 63 (2001) 021902
    • (2001) Phys. Rev. E , vol.63 , pp. 021902
    • Yao, W.1    Yu, P.2    Essex, C.3
  • 20
    • 0040036617 scopus 로고    scopus 로고
    • Simplest normal forms of Hopf and generalized Hopf bifurcations
    • Yu P. Simplest normal forms of Hopf and generalized Hopf bifurcations. Int. J. Bifurcat. Chaos 9 (1999) 1917-1939
    • (1999) Int. J. Bifurcat. Chaos , vol.9 , pp. 1917-1939
    • Yu, P.1
  • 21
    • 0000950086 scopus 로고
    • Center manifold theory in infinite dimension
    • Vanderbauwhede A., and Ioos G. Center manifold theory in infinite dimension. Dynam. Rep. 2 (1992)
    • (1992) Dynam. Rep. , vol.2
    • Vanderbauwhede, A.1    Ioos, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.