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Volumn 28, Issue 1, 2002, Pages 1-21

Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

Author keywords

G.1.0 Numerical analysis : General numerical algorithms; G.1.4 Numerical analysis : Quadrature and Numerical Differentiation; G.1.7 Numerical analysis : Ordinary Differential Equations multistep and multivalue methods

Indexed keywords


EID: 0039483059     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/513001.513002     Document Type: Article
Times cited : (687)

References (32)
  • 2
    • 0023362493 scopus 로고
    • Periodic solutions in a model of recurrent neural feedback
    • CASTELFRANCO, A. M. AND STECH, H. W. 1987. Periodic solutions in a model of recurrent neural feedback. SIAM J. Appl. Math. 47, 3, 573-588.
    • (1987) SIAM J. Appl. Math. , vol.47 , Issue.3 , pp. 573-588
    • Castelfranco, A.M.1    Stech, H.W.2
  • 3
    • 0031212575 scopus 로고    scopus 로고
    • DKLAG6: A code based on continuously imbedded sixth order Runge-Kutta methods for the solution of state dependent functional differential equations
    • CORWIN, S. P., SARAFYAN, D., AND THOMPSON, S. 1997. DKLAG6: A code based on continuously imbedded sixth order Runge-Kutta methods for the solution of state dependent functional differential equations. Appl. Numer. Math. 24, 2-3, 319-330.
    • (1997) Appl. Numer. Math. , vol.24 , Issue.2-3 , pp. 319-330
    • Corwin, S.P.1    Sarafyan, D.2    Thompson, S.3
  • 6
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions
    • DOEDEL, E. J., KELLER, H. B., AND KERNEVEZ, J. P. 1991a. Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions. Internat. J. Bifur. Chaos 1, 3, 493-520.
    • (1991) Internat. J. Bifur. Chaos , vol.1 , Issue.3 , pp. 493-520
    • Doedel, E.J.1    Keller, H.B.2    Kernevez, J.P.3
  • 7
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems (II) bifurcation in infinite dimensions
    • DOEDEL, E. J., KELLER, H. B., AND KERNEVEZ, J. P. 1991b. Numerical analysis and control of bifurcation problems (II) bifurcation in infinite dimensions. Internat. J. Bifur. Chaos 1, 4, 745-772.
    • (1991) Internat. J. Bifur. Chaos , vol.1 , Issue.4 , pp. 745-772
    • Doedel, E.J.1    Keller, H.B.2    Kernevez, J.P.3
  • 10
    • 0036627555 scopus 로고    scopus 로고
    • Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations
    • DOI 10.1007/S002110100313
    • ENGELBORGHS, K. AND DOEDEL, E. 2001. Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations. Numerische Mathematik; DOI 10.1007/S002110100313.
    • (2001) Numerische Mathematik
    • Engelborghs, K.1    Doedel, E.2
  • 11
    • 0034770393 scopus 로고    scopus 로고
    • Collocation methods for the computation of periodic solutions of delay differential equations
    • ENGELBORGHS, K., LUZYANINA, T., IN 'T HOUT, K. J., AND ROOSE, D. 2000a. Collocation methods for the computation of periodic solutions of delay differential equations. SIAM J. Sci. Comput. 22, 5, 1593-1609.
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.5 , pp. 1593-1609
    • Engelborghs, K.1    Luzyanina, T.2    In 't Hout, K.J.3    Roose, D.4
  • 12
    • 0034509217 scopus 로고    scopus 로고
    • Numerical bifurcation analysis of delay differential equations
    • ENGELBORGHS, K., LUZYANINA, T., AND ROOSE, D. 2000b. Numerical bifurcation analysis of delay differential equations. J. Comput. Appl. Math. 125, 1-2, 265-275.
    • (2000) J. Comput. Appl. Math. , vol.125 , Issue.1-2 , pp. 265-275
    • Engelborghs, K.1    Luzyanina, T.2    Roose, D.3
  • 14
    • 0012637308 scopus 로고    scopus 로고
    • Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations
    • ENGELBORGHS, K. AND ROOSE, D. 1999. Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations. Adv. Comput. Math. 10, 3-4, 271-289.
    • (1999) Adv. Comput. Math. , vol.10 , Issue.3-4 , pp. 271-289
    • Engelborghs, K.1    Roose, D.2
  • 15
    • 0040142621 scopus 로고    scopus 로고
    • On stability of LMS-methods and characteristic roots of delay differential equations
    • ENGELBORGHS, K. AND ROOSE, D. 2001. On stability of LMS-methods and characteristic roots of delay differential equations. SIAM J. Num. Analysis.
    • (2001) SIAM J. Num. Analysis
    • Engelborghs, K.1    Roose, D.2
  • 19
    • 0003346959 scopus 로고
    • Theory of functional differential equations
    • Springer-Verlag
    • HALE, J. K. 1977. Theory of Functional Differential Equations. Applied Mathematical Sciences, vol. 3. Springer-Verlag.
    • (1977) Applied Mathematical Sciences , vol.3
    • Hale, J.K.1
  • 20
    • 0003324723 scopus 로고
    • Introduction to functional differential equations
    • Springer-Verlag
    • HALE, J. K. AND VERDUYN LUNEL, S. M. 1993. Introduction to Functional Differential Equations. Applied Mathematical Sciences, vol. 99. Springer-Verlag.
    • (1993) Applied Mathematical Sciences , vol.99
    • Hale, J.K.1    Verduyn Lunel, S.M.2
  • 21
    • 0010706645 scopus 로고
    • A code for Hopf bifurcation analysis of autonomous delay-differential systems
    • Oscillations, Bifurcations and Chaos, F. V. Atkinson, W. F. Langford, and A. B. Mingarelli, Eds. Amer. Math. Soc., Providence, RI
    • HASSARD, B. D. 1987. A code for Hopf bifurcation analysis of autonomous delay-differential systems. In Oscillations, Bifurcations and Chaos, F. V. Atkinson, W. F. Langford, and A. B. Mingarelli, Eds. Can. Math. Soc. Conference Proceedings, vol. 8. Amer. Math. Soc., Providence, RI, 447-463.
    • (1987) Can. Math. Soc. Conference Proceedings , vol.8 , pp. 447-463
    • Hassard, B.D.1
  • 22
    • 0008655094 scopus 로고    scopus 로고
    • The numerical stability of linear multistep methods for delay differential equations with many delays
    • HONG-JIONG, T. AND JIAO-XUN, K. 1996. The numerical stability of linear multistep methods for delay differential equations with many delays. SIAM J. Numer. Anal. 33, 3, 883-889.
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.3 , pp. 883-889
    • Hong-Jiong, T.1    Jiao-Xun, K.2
  • 23
    • 0003310684 scopus 로고    scopus 로고
    • Introduction to the theory and application of functional differential equations
    • Kluwer Academic Publishers
    • KOLMANOVSKII, V. B. AND MYSHKIS, A. 1999. Introduction to the Theory and Application of Functional Differential Equations. Mathematics and its Applications, vol. 463. Kluwer Academic Publishers.
    • (1999) Mathematics and Its Applications , vol.463
    • Kolmanovskii, V.B.1    Myshkis, A.2
  • 24
    • 0003236870 scopus 로고
    • Elements of applied bifurcation theory
    • Springer-Verlag
    • KUZNETSOV, Y. A. 1995. Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol. 112. Springer-Verlag.
    • (1995) Applied Mathematical Sciences , vol.112
    • Kuznetsov, Y.A.1
  • 25
    • 0040736745 scopus 로고    scopus 로고
    • Computing Floquet multipliers for functional differential equations
    • LUZYANINA, T. AND ENGELBORGHS, K. 2001. Computing Floquet multipliers for functional differential equations. Internat. J. Bifur. Chaos.
    • (2001) Internat. J. Bifur. Chaos
    • Luzyanina, T.1    Engelborghs, K.2
  • 26
    • 0030215653 scopus 로고    scopus 로고
    • Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
    • LUZYANINA, T. AND ROOSE, D. 1996. Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations. J. Comput. Appl. Math. 72, 379-392.
    • (1996) J. Comput. Appl. Math. , vol.72 , pp. 379-392
    • Luzyanina, T.1    Roose, D.2
  • 28
    • 0019526830 scopus 로고
    • A fitzHugh differential-difference equation modeling recurrent neural feedback
    • PLANT, R. E. 1981. A FitzHugh differential-difference equation modeling recurrent neural feedback. SIAM J. Appl. Math. 40, 1, 150-162.
    • (1981) SIAM J. Appl. Math. , vol.40 , Issue.1 , pp. 150-162
    • Plant, R.E.1
  • 29
    • 0000068964 scopus 로고    scopus 로고
    • Time delay induced death in coupled limit cycle oscillators
    • REDDY, D. V. R., SEN, A., AND JOHNSTON, G. L. 1998. Time delay induced death in coupled limit cycle oscillators. Phys. Rev. Lett. 80, 5109-5112.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 5109-5112
    • Reddy, D.V.R.1    Sen, A.2    Johnston, G.L.3
  • 30
    • 0347963951 scopus 로고    scopus 로고
    • Time delay effects on coupled limit cycle oscillators at Hopf bifurcation
    • REDDY, D. V. R., SEN, A., AND JOHNSTON, G. L. 1999. Time delay effects on coupled limit cycle oscillators at Hopf bifurcation. Physica D 129, 15-34.
    • (1999) Physica D , vol.129 , pp. 15-34
    • Reddy, D.V.R.1    Sen, A.2    Johnston, G.L.3
  • 31
    • 85097992588 scopus 로고
    • Practical bifurcation and stability analysis - From equilibrium to chaos, 2nd ed
    • Springer-Verlag Berlin
    • SEYDEL, R. 1994. Practical Bifurcation and Stability Analysis - From Equilibrium to Chaos, 2nd ed. Interdisciplinary Applied Mathematics, vol. 5. Springer-Verlag Berlin.
    • (1994) Interdisciplinary Applied Mathematics , vol.5
    • Seydel, R.1
  • 32
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays
    • SHAYER, L. P. AND CAMPBELL, S. A. 2000. Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays. SIAM J. Appl. Math. 61, 2, 673-700.
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.2 , pp. 673-700
    • Shayer, L.P.1    Campbell, S.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.