메뉴 건너뛰기




Volumn 125, Issue 1-2, 2000, Pages 265-275

Numerical bifurcation analysis of delay differential equations

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CONVERGENCE OF NUMERICAL METHODS; THEOREM PROVING;

EID: 0034509217     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00472-6     Document Type: Article
Times cited : (62)

References (26)
  • 1
    • 0000381963 scopus 로고
    • On the zeros of exponential polynomials
    • C.E. Avellar, J.K. Hale, On the zeros of exponential polynomials, J. Math. Anal. Appl. 73 (1980) 434-452.
    • (1980) J. Math. Anal. Appl. , vol.73 , pp. 434-452
    • Avellar, C.E.1    Hale, J.K.2
  • 2
    • 0023362493 scopus 로고
    • Periodic solutions in a model of recurrent neural feedback
    • A.M. Castelfranco, H.W. Stech, Periodic solutions in a model of recurrent neural feedback, SIAM J. Appl. Math. 47 (3) (1987) 573-588.
    • (1987) SIAM J. Appl. Math. , vol.47 , Issue.3 , pp. 573-588
    • Castelfranco, A.M.1    Stech, H.W.2
  • 3
    • 0000757329 scopus 로고
    • A numerical technique for bifurcation problems in delay differential equations
    • Proceedings of the 11th Manitoba Conference on Num. Math. Comput, University of Manitoba, Winnipeg, Canada
    • E.J. Doedel, P.P.C. Leung, A numerical technique for bifurcation problems in delay differential equations, Congr. Num. 34 (1982) 225-237 (Proceedings of the 11th Manitoba Conference on Num. Math. Comput, University of Manitoba, Winnipeg, Canada).
    • (1982) Congr. Num. , vol.34 , pp. 225-237
    • Doedel, E.J.1    Leung, P.P.C.2
  • 4
    • 0003261196 scopus 로고
    • Introduction to the theory and application of differential equations with deviating arguments
    • Academic Press, New York
    • L.E. El'sgol'ts, H.W. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Mathematics in Science and Engineering, Vol. 105, Academic Press, New York, 1973.
    • (1973) Mathematics in Science and Engineering , vol.105
    • El'sgol'ts, L.E.1    Norkin, H.W.2
  • 6
    • 0012637308 scopus 로고    scopus 로고
    • Numerical computation of stability and detection of Hopf bifurcations of steady-state solutions of delay differential equations
    • K. Engelborghs, D. Roose, Numerical computation of stability and detection of Hopf bifurcations of steady-state solutions of delay differential equations, Adv. Comput. Math. 10 (3-4) (1999) 271-289.
    • (1999) Adv. Comput. Math. , vol.10 , Issue.3-4 , pp. 271-289
    • Engelborghs, K.1    Roose, D.2
  • 7
    • 0033191768 scopus 로고    scopus 로고
    • Smoothness loss of periodic solutions of a neutral functional differential equation: On a bifurcation of the essential spectrum
    • K. Engelborghs, D. Roose, Smoothness loss of periodic solutions of a neutral functional differential equation: on a bifurcation of the essential spectrum, Dynamics Stability Systems 14 (3) (1999) 255-273.
    • (1999) Dynamics Stability Systems , vol.14 , Issue.3 , pp. 255-273
    • Engelborghs, K.1    Roose, D.2
  • 8
    • 0040598878 scopus 로고    scopus 로고
    • Bifurcation analysis of periodic solutions of neutral functional differential equations: A case study
    • K. Engelborghs, D. Roose, T. Luzyanina, Bifurcation analysis of periodic solutions of neutral functional differential equations: a case study, Int. J. Bifurc. Chaos 8 (10) (1998) 1889-1905.
    • (1998) Int. J. Bifurc. Chaos , vol.8 , Issue.10 , pp. 1889-1905
    • Engelborghs, K.1    Roose, D.2    Luzyanina, T.3
  • 11
    • 0037860065 scopus 로고    scopus 로고
    • Numerical Hopf bifurcation for a class of delay differential equations
    • V. Wulf, N.J. Ford, Numerical Hopf bifurcation for a class of delay differential equations, J. Comput. Appl. Math. 115 (1-2) (2000) 601-616.
    • (2000) J. Comput. Appl. Math. , vol.115 , Issue.1-2 , pp. 601-616
    • Wulf, V.1    Ford, N.J.2
  • 12
    • 0001550896 scopus 로고    scopus 로고
    • Parameter domains for instability of uniform states in systems with many delays
    • S.A. Gourley, M.V. Bartuccelli, Parameter domains for instability of uniform states in systems with many delays, J. Math. Biol. 35 (1997) 843-867.
    • (1997) J. Math. Biol. , vol.35 , pp. 843-867
    • Gourley, S.A.1    Bartuccelli, M.V.2
  • 13
    • 34250250639 scopus 로고
    • Effective computation of periodic orbits and bifurcation diagrams in delay equations
    • K.P. Hadeler, Effective computation of periodic orbits and bifurcation diagrams in delay equations, Numer. Math. 34 (1980) 457-467.
    • (1980) Numer. Math. , vol.34 , pp. 457-467
    • Hadeler, K.P.1
  • 14
    • 0343358890 scopus 로고
    • Theory of Functional Differential Equations, Springer, Berlin
    • J.K. Hale, in: Theory of Functional Differential Equations, Applied Mathematical Sciences, Vol. 3, Springer, Berlin, 1977.
    • (1977) Applied Mathematical Sciences , vol.3
    • Hale, J.K.1
  • 15
    • 0343358890 scopus 로고
    • Introduction to Functional Differential Equations, Springer, Berlin
    • J.K. Hale, S.M. Verduyn Lunel, in: Introduction to Functional Differential Equations, Applied Mathematical Sciences, Vol. 99, Springer, Berlin, 1993.
    • (1993) Applied Mathematical Sciences , vol.99
    • Hale, J.K.1    Verduyn Lunel, S.M.2
  • 16
    • 0010706645 scopus 로고
    • A code for Hopf bifurcation analysis of autonomous delay-differential systems
    • W.F. Langford, F.V. Atkinson, A.B. Mingarelli (Eds.), Amer. Math. Soc., Providence, RI
    • B.D. Hassard, A code for Hopf bifurcation analysis of autonomous delay-differential systems, in: W.F. Langford, F.V. Atkinson, A.B. Mingarelli (Eds.), Oscillations, Bifurcations and Chaos, Canadian Mathematical Society Conference Proceedings, Vol. 8, Amer. Math. Soc., Providence, RI, 1987, pp. 447-463.
    • (1987) Oscillations, Bifurcations and Chaos, Canadian Mathematical Society Conference Proceedings , vol.8 , pp. 447-463
    • Hassard, B.D.1
  • 18
    • 39549090968 scopus 로고    scopus 로고
    • Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system
    • L. Dugard, E.I. Verriest (Eds.), Stability and Control of Time-Delay Systems, Springer, Berlin
    • J. Louisell, in: L. Dugard, E.I. Verriest (Eds.), Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system, Stability and Control of Time-Delay Systems, Lecture Notes in Control and Information Sciences, Vol. 228, Springer, Berlin, 1997.
    • (1997) Lecture Notes in Control and Information Sciences , vol.228
    • Louisell, J.1
  • 19
    • 0031279807 scopus 로고    scopus 로고
    • Computation, continuation and bifurcation analysis of periodic solutions of delay differential equations
    • T. Luzyanina, K. Engelborghs, K. Lust, D. Roose, Computation, continuation and bifurcation analysis of periodic solutions of delay differential equations, Int. J. Bifurc. Chaos 7 (11) (1997) 2547-2560.
    • (1997) Int. J. Bifurc. Chaos , vol.7 , Issue.11 , pp. 2547-2560
    • Luzyanina, T.1    Engelborghs, K.2    Lust, K.3    Roose, D.4
  • 20
    • 0030215653 scopus 로고    scopus 로고
    • Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
    • T. Luzyanina, D. Roose, Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations, J. Comput. Appl. Math. 72 (1996) 379-392.
    • (1996) J. Comput. Appl. Math. , vol.72 , pp. 379-392
    • Luzyanina, T.1    Roose, D.2
  • 21
    • 0030500518 scopus 로고    scopus 로고
    • Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems
    • K. Meerbergen, D. Roose, Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems, IMA J. Numer. Anal. 16 (1996) 297-346.
    • (1996) IMA J. Numer. Anal. , vol.16 , pp. 297-346
    • Meerbergen, K.1    Roose, D.2
  • 23
    • 0019526830 scopus 로고
    • A FitzHugh differential-difference equation modeling recurrent neural feedback
    • R.E. Plant, A FitzHugh differential-difference equation modeling recurrent neural feedback, SIAM J. Appl. Math. 40 (1) (1981) 150-162.
    • (1981) SIAM J. Appl. Math. , vol.40 , Issue.1 , pp. 150-162
    • Plant, R.E.1
  • 26
    • 0034515399 scopus 로고    scopus 로고
    • Retarded differential equations
    • C.T.H. Baker, Retarded differential equations, J. Comput. Appl. Math. 125 (2000) 309-335.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 309-335
    • Baker, C.T.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.