메뉴 건너뛰기




Volumn 2, Issue , 2002, Pages 149-219

Chapter 4 Numerical continuation, and computation of normal forms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0038228324     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80025-X     Document Type: Chapter
Times cited : (139)

References (77)
  • 1
    • 70350662980 scopus 로고    scopus 로고
    • Numerical path following
    • Ciarlet P.G., Lions J.L., and Lions J.L. (Eds), North-Holland, Amsterdam
    • Allgower E.L., and Georg K. Numerical path following. In: Ciarlet P.G., Lions J.L., and Lions J.L. (Eds). Handbook of Numerical Analysis Vol. 5 (1996), North-Holland, Amsterdam
    • (1996) Handbook of Numerical Analysis , vol.5
    • Allgower, E.L.1    Georg, K.2
  • 2
    • 0001679106 scopus 로고
    • Collocation software for boundary value differential-algebraic equations
    • Ascher U.M., and Spiteri R.J. Collocation software for boundary value differential-algebraic equations. SIAM J. Sci. Comput. 15 (1995) 938-952
    • (1995) SIAM J. Sci. Comput. , vol.15 , pp. 938-952
    • Ascher, U.M.1    Spiteri, R.J.2
  • 3
    • 84968466504 scopus 로고
    • A collocation solver for mixed order systems of boundary value problems
    • Ascher U.M., Christiansen J., and Russell R.D. A collocation solver for mixed order systems of boundary value problems. Math. Comp. 33 (1979) 659-679
    • (1979) Math. Comp. , vol.33 , pp. 659-679
    • Ascher, U.M.1    Christiansen, J.2    Russell, R.D.3
  • 4
    • 0030405090 scopus 로고    scopus 로고
    • Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two
    • Bai F., and Champneys A.R. Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two. Dynam. Stability Systems 11 (1996) 325-346
    • (1996) Dynam. Stability Systems , vol.11 , pp. 325-346
    • Bai, F.1    Champneys, A.R.2
  • 5
    • 67649350557 scopus 로고    scopus 로고
    • Numerical solution of parameter dependent two-point boundary value problems using deferred correction
    • Department of Mathematics, Imperial College, London
    • Bashir-Ali Z. Numerical solution of parameter dependent two-point boundary value problems using deferred correction. Ph.D. thesis (1998), Department of Mathematics, Imperial College, London
    • (1998) Ph.D. thesis
    • Bashir-Ali, Z.1
  • 6
    • 0002433039 scopus 로고
    • Global bifurcations and their numerical computation
    • Roose D., Spence A., and Dier B.D. (Eds), Kluwer, Dordrecht
    • Beyn W.-J. Global bifurcations and their numerical computation. In: Roose D., Spence A., and Dier B.D. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications (1990), Kluwer, Dordrecht 169-181
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 169-181
    • Beyn, W.-J.1
  • 7
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • Beyn W.-J. The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Anal. 10 (1990) 379-405
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 379-405
    • Beyn, W.-J.1
  • 8
    • 0000339206 scopus 로고
    • Numerical methods for dynamical systems
    • Nonlinear Partial Differential Equations and Dynamical Systems. Light W. (Ed), Oxford Univ. Press, Oxford
    • Beyn W.-J. Numerical methods for dynamical systems. In: Light W. (Ed). Nonlinear Partial Differential Equations and Dynamical Systems. Advances in Numerical Analysis Vol. I (1991), Oxford Univ. Press, Oxford 175-236
    • (1991) Advances in Numerical Analysis , vol.I , pp. 175-236
    • Beyn, W.-J.1
  • 9
    • 21844504535 scopus 로고
    • Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point
    • Beyn W.-J. Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA J. Numer. Anal. 14 (1994) 381-410
    • (1994) IMA J. Numer. Anal. , vol.14 , pp. 381-410
    • Beyn, W.-J.1
  • 10
    • 21144451973 scopus 로고
    • Stationary solutions of a system of ordinary differential equations depending upon a parameter
    • in Russian, Research Computing Centre, USSR Academy of Sciences, Pushchino
    • in Russian. Borisyuk R.M. Stationary solutions of a system of ordinary differential equations depending upon a parameter. FORTRAN Software Series Vol. 6 (1981), Research Computing Centre, USSR Academy of Sciences, Pushchino
    • (1981) FORTRAN Software Series , vol.6
    • Borisyuk, R.M.1
  • 11
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homo-clinic bifurcations
    • Champneys A.R., and Kuznetsov Y.A. Numerical detection and continuation of codimension-two homo-clinic bifurcations. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 4 (1994) 795-822
    • (1994) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.4 , pp. 795-822
    • Champneys, A.R.1    Kuznetsov, Y.A.2
  • 13
    • 0020807390 scopus 로고
    • Amplitude equations for systems with competing instabilities
    • Coullet P.H., and Spiegel E.A. Amplitude equations for systems with competing instabilities. SIAM J. Appl. Math. 43 (1983) 776-821
    • (1983) SIAM J. Appl. Math. , vol.43 , pp. 776-821
    • Coullet, P.H.1    Spiegel, E.A.2
  • 14
    • 0000319158 scopus 로고
    • Collocation at Gaussian points
    • Boor C.d., and Swartz B. Collocation at Gaussian points. SIAM J. Numer. Anal. 10 (1973) 582-606
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 582-606
    • Boor, C.d.1    Swartz, B.2
  • 15
    • 0000025015 scopus 로고
    • Homoclinic bifurcations with nonhyperbolic equilibria
    • Deng B. Homoclinic bifurcations with nonhyperbolic equilibria. SIAM J. Math. Anal. 21 (1990) 693-720
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 693-720
    • Deng, B.1
  • 16
    • 0023401540 scopus 로고
    • Efficient numerical pathfollowing beyond critical points
    • Deuflhard P., Fiedler B., and Kunkel P. Efficient numerical pathfollowing beyond critical points. SIAM J. Numer. Anal. 24 (1987) 912-927
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 912-927
    • Deuflhard, P.1    Fiedler, B.2    Kunkel, P.3
  • 17
    • 0001755071 scopus 로고
    • AUTO a program for the automatic bifurcation analysis of autonomous systems
    • Doedel E.J. AUTO a program for the automatic bifurcation analysis of autonomous systems. Congr. Nu-mer. 30 (1981) 265-384
    • (1981) Congr. Nu-mer. , vol.30 , pp. 265-384
    • Doedel, E.J.1
  • 18
    • 67649301684 scopus 로고    scopus 로고
    • Numerical analysis of bifurcation problems
    • 1997 and 1999, Hamburg-Harburg Summer Schools
    • 1997 and 1999. Doedel E.J. Numerical analysis of bifurcation problems. Technical report (1999), Hamburg-Harburg Summer Schools. http://ftp.cs.concordia.ca.pub/doedel/doc/hamburg.ps.Z
    • (1999) Technical report
    • Doedel, E.J.1
  • 22
    • 0031504868 scopus 로고    scopus 로고
    • Successive continuation for locating connecting orbits
    • Doedel E.J., Friedman M.J., and Kunin B.I. Successive continuation for locating connecting orbits. Numer. Algorithms 14 (1997) 103-124
    • (1997) Numer. Algorithms , vol.14 , pp. 103-124
    • Doedel, E.J.1    Friedman, M.J.2    Kunin, B.I.3
  • 24
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems: (I) Bifurcation in finite dimensions
    • Doedel E.J., Keller H.B., and Kernévez J.-P. Numerical analysis and control of bifurcation problems: (I) Bifurcation in finite dimensions. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 1 (1991) 493-520
    • (1991) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.1 , pp. 493-520
    • Doedel, E.J.1    Keller, H.B.2    Kernévez, J.-P.3
  • 25
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems: (II) Bifurcation in infinite dimensions
    • Doedel E.J., Keller H.B., and Kernévez J.-P. Numerical analysis and control of bifurcation problems: (II) Bifurcation in infinite dimensions. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 1 (1991) 745-772
    • (1991) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.1 , pp. 745-772
    • Doedel, E.J.1    Keller, H.B.2    Kernévez, J.-P.3
  • 26
    • 0002232810 scopus 로고
    • A simple global characterization for normal forms of singular vector fields
    • Elphick C., Tirapegui E., Brächet M.E., Coullet P.H., and Iooss G. A simple global characterization for normal forms of singular vector fields. Phys. D 32 (1987) 95-127
    • (1987) Phys. D , vol.32 , pp. 95-127
    • Elphick, C.1    Tirapegui, E.2    Brächet, M.E.3    Coullet, P.H.4    Iooss, G.5
  • 28
    • 0342924582 scopus 로고    scopus 로고
    • Global pathfollowing of homoclinic orbits in two-parameter flows
    • Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds), Longman, Harlow
    • Fiedler B. Global pathfollowing of homoclinic orbits in two-parameter flows. In: Dangelmayr G., Fiedler B., Kirchgässner K., and Mielke A. (Eds). Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation and Stability. Pitman Res. Notes Math. Ser. Vol. 352 (1996), Longman, Harlow
    • (1996) Pitman Res. Notes Math. Ser. , vol.352
    • Fiedler, B.1
  • 29
    • 0011311010 scopus 로고
    • Numerical analysis and accurate computation of heteroclinic orbits in the case of centre manifolds
    • Friedman M.J. Numerical analysis and accurate computation of heteroclinic orbits in the case of centre manifolds. J. Dynamics Differential Equations 5 (1993) 59-87
    • (1993) J. Dynamics Differential Equations , vol.5 , pp. 59-87
    • Friedman, M.J.1
  • 30
    • 0001964150 scopus 로고
    • Condition for a matrix to have only characteristic roots with negative real parts
    • Fuller A.T. Condition for a matrix to have only characteristic roots with negative real parts. J. Math. Anal. Appl. 23 (1968) 71-98
    • (1968) J. Math. Anal. Appl. , vol.23 , pp. 71-98
    • Fuller, A.T.1
  • 31
    • 0002895479 scopus 로고
    • Local birth of homoclinic chaos
    • Gaspard P. Local birth of homoclinic chaos. Phys. D 62 (1993) 94-122
    • (1993) Phys. D , vol.62 , pp. 94-122
    • Gaspard, P.1
  • 33
    • 0042470959 scopus 로고
    • Mixed block elimination for linear systems with wider borders
    • Govaerts W., and Pryce J.D. Mixed block elimination for linear systems with wider borders. IMA J. Numer. Anal. 13 (1993) 161-180
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 161-180
    • Govaerts, W.1    Pryce, J.D.2
  • 35
    • 0000856944 scopus 로고
    • The calculation of Hopf points by a direct method
    • Griewank A., and Reddien G.W. The calculation of Hopf points by a direct method. IMA J. Numer. Anal. 3 (1983) 295-303
    • (1983) IMA J. Numer. Anal. , vol.3 , pp. 295-303
    • Griewank, A.1    Reddien, G.W.2
  • 36
    • 38249023149 scopus 로고
    • Computation of cusp singularities for operator equations and their dis-cretizations
    • Griewank A., and Reddien G.W. Computation of cusp singularities for operator equations and their dis-cretizations. J. Comput. Appl. Math. 26 (1989) 133-153
    • (1989) J. Comput. Appl. Math. , vol.26 , pp. 133-153
    • Griewank, A.1    Reddien, G.W.2
  • 37
    • 0040248721 scopus 로고    scopus 로고
    • Computing Hopf bifurcations. II. Three examples from neurophysiology
    • Guckenheimer J., and Myers M. Computing Hopf bifurcations. II. Three examples from neurophysiology. SIAM J. Sci. Comput. 17 (1996) 1275-1301
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1275-1301
    • Guckenheimer, J.1    Myers, M.2
  • 38
    • 0003044873 scopus 로고
    • Introduction to dynamic bifurcation
    • Bifurcation Theory and Applications. Salvadori L. (Ed), Springer, Berlin
    • Hale J.K. Introduction to dynamic bifurcation. In: Salvadori L. (Ed). Bifurcation Theory and Applications. Lecture Notes in Math. Vol. 1057 (1983), Springer, Berlin 106-151
    • (1983) Lecture Notes in Math. , vol.1057 , pp. 106-151
    • Hale, J.K.1
  • 39
    • 0011314250 scopus 로고
    • Computation of invariant manifolds
    • Holmes P.J. (Ed), SIAM, Philadelphia, PA
    • Hassard B.D. Computation of invariant manifolds. In: Holmes P.J. (Ed). New Approaches to Nonlinear Problems in Dynamics (1980), SIAM, Philadelphia, PA 27-42
    • (1980) New Approaches to Nonlinear Problems in Dynamics , pp. 27-42
    • Hassard, B.D.1
  • 41
    • 0012853542 scopus 로고
    • DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
    • Holodniok M., and Kubiček M. DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations. J. Comput. Phys. 55 (1984) 254-267
    • (1984) J. Comput. Phys. , vol.55 , pp. 254-267
    • Holodniok, M.1    Kubiček, M.2
  • 42
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • Rabinowitz P. (Ed), Academic Press, New York
    • Keller H.B. 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.B.1
  • 43
    • 0003394350 scopus 로고
    • Notes by A.K. Nandakumaran and M. Ramaswamy, Indian Institute of Science, Bangalore, Springer, Berlin
    • Notes by A.K. Nandakumaran and M. Ramaswamy, Indian Institute of Science, Bangalore. Keller H.B. Lectures on Numerical Methods in Bifurcation Problems (1987), Springer, Berlin
    • (1987) Lectures on Numerical Methods in Bifurcation Problems
    • Keller, H.B.1
  • 45
    • 0003316491 scopus 로고
    • LINLBF: A program for continuation and bifurcation analysis of equilibria up to codimension three
    • Roose D., Dier B.D., and Spence A. (Eds), Kluwer, Dordrecht
    • Khibnik A.I. LINLBF: A program for continuation and bifurcation analysis of equilibria up to codimension three. In: Roose D., Dier B.D., and Spence A. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications (1990), Kluwer, Dordrecht 283-296
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 283-296
    • Khibnik, A.I.1
  • 46
    • 4544313738 scopus 로고
    • Continuation techniques and interactive soft-ware for bifurcation analysis of ODEs and iterated maps
    • Khibnik A.I., Kuznetsov Y., Levitin V.V., and Nikolaev E.V. Continuation techniques and interactive soft-ware for bifurcation analysis of ODEs and iterated maps. Phys. D 62 (1993) 360-371
    • (1993) Phys. D , vol.62 , pp. 360-371
    • Khibnik, A.I.1    Kuznetsov, Y.2    Levitin, V.V.3    Nikolaev, E.V.4
  • 48
    • 0011326523 scopus 로고
    • One-dimensional invariant manifolds in ordinary differential equations depending upon parameters
    • in Russian, Research Computing Centre, USSR Academy of Sciences, Pushchino
    • in Russian. Kuznetsov Y.A. One-dimensional invariant manifolds in ordinary differential equations depending upon parameters. FORTRAN Software Series Vol. 8 (1983), Research Computing Centre, USSR Academy of Sciences, Pushchino
    • (1983) FORTRAN Software Series , vol.8
    • Kuznetsov, Y.A.1
  • 53
    • 0030621838 scopus 로고    scopus 로고
    • Computation and continuation of homoclinic and heteroclinic orbits with arclength parametrizations
    • Liu L., Moore G., and Russell R.D. Computation and continuation of homoclinic and heteroclinic orbits with arclength parametrizations. SIAM J. Sci. Comput. 18 (1997) 69-93
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 69-93
    • Liu, L.1    Moore, G.2    Russell, R.D.3
  • 54
    • 0141871098 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems: a rational spectral approach
    • Liu Y., Liu L., and Tang T. The numerical computation of connecting orbits in dynamical systems: a rational spectral approach. J. Comput. Phys. 111 (1994) 373-380
    • (1994) J. Comput. Phys. , vol.111 , pp. 373-380
    • Liu, Y.1    Liu, L.2    Tang, T.3
  • 56
    • 0024620677 scopus 로고
    • A numerical approximation for the simple bifurcation points
    • Mei Z. A numerical approximation for the simple bifurcation points. Numer. Funct. Anal. Optimiz. 10 (1989) 383-400
    • (1989) Numer. Funct. Anal. Optimiz. , vol.10 , pp. 383-400
    • Mei, Z.1
  • 57
    • 0001834849 scopus 로고
    • On the stability of the center for time periodic perturbations
    • Melnikov V.K. On the stability of the center for time periodic perturbations. Trans. Moscow Math. Soc. 12 (1963) 1-57
    • (1963) Trans. Moscow Math. Soc. , vol.12 , pp. 1-57
    • Melnikov, V.K.1
  • 58
    • 0019265087 scopus 로고
    • The numerical treatment of non-trivial bifurcation points
    • Moore G. The numerical treatment of non-trivial bifurcation points. Numer. Funct. Anal. Optimiz. 2 (1980) 441-472
    • (1980) Numer. Funct. Anal. Optimiz. , vol.2 , pp. 441-472
    • Moore, G.1
  • 59
    • 21844508391 scopus 로고
    • Computation and parametrisation of periodic and connecting orbits
    • Moore G. Computation and parametrisation of periodic and connecting orbits. IMA J. Numer. Anal. 15 (1995) 319-331
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 319-331
    • Moore, G.1
  • 60
    • 0000863468 scopus 로고
    • The calculation of turning points of nonlinear equations
    • Moore G., and Spence A. The calculation of turning points of nonlinear equations. SIAM J. Numer. Anal. 17 (1980) 567-576
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 567-576
    • Moore, G.1    Spence, A.2
  • 61
    • 0001747859 scopus 로고
    • On dynamical systems close to Hamiltonian systems
    • in Russian
    • in Russian. Pontryagin L.S. On dynamical systems close to Hamiltonian systems. J. Exptl. Theoret. Phys. 4 (1934) 234-238
    • (1934) J. Exptl. Theoret. Phys. , vol.4 , pp. 234-238
    • Pontryagin, L.S.1
  • 63
    • 84976786620 scopus 로고
    • Algorithm 596: A program for a locally-parametrized continuation process
    • Rheinboldt W.C., and Burkardt J.V. Algorithm 596: A program for a locally-parametrized continuation process. ACM Trans. Math. Software 9 (1983) 236-241
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 236-241
    • Rheinboldt, W.C.1    Burkardt, J.V.2
  • 64
    • 0001588095 scopus 로고
    • A method for homoclinic and heteroclinic continuation in two and three dimensions
    • Roose D., Spence A., and Dier B.D. (Eds), Kluwer, Dordrecht
    • Rodríguez-Luis A.J., Freire E., and Ponce E. A method for homoclinic and heteroclinic continuation in two and three dimensions. In: Roose D., Spence A., and Dier B.D. (Eds). Continuation and Bifurcations: Numerical Techniques and Applications (1990), Kluwer, Dordrecht 197-210
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 197-210
    • Rodríguez-Luis, A.J.1    Freire, E.2    Ponce, E.3
  • 65
    • 0040232467 scopus 로고
    • Numerical computation of origins for Hopf bifurcations in a two-parameter problem
    • Küpper T., Seydel R., and Troger H. (Eds), Birkhäuser, Basel
    • Roose D. Numerical computation of origins for Hopf bifurcations in a two-parameter problem. In: Küpper T., Seydel R., and Troger H. (Eds). Bifurcation: Analysis, Algorithms, Applications (1987), Birkhäuser, Basel 268-273
    • (1987) Bifurcation: Analysis, Algorithms, Applications , pp. 268-273
    • Roose, D.1
  • 66
    • 0022414874 scopus 로고
    • A direct method for the computation of Hopf bifurcation points
    • Roose D., and Hlavacek V. A direct method for the computation of Hopf bifurcation points. SIAM J. Appl. Math. 45 (1985) 897-994
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 897-994
    • Roose, D.1    Hlavacek, V.2
  • 67
    • 0002102436 scopus 로고
    • Adaptive mesh selection strategies for solving boundary value problems
    • Russell R.D., and Christiansen J. Adaptive mesh selection strategies for solving boundary value problems. SIAM J. Numer. Anal. 15 (1978) 59-80
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 59-80
    • Russell, R.D.1    Christiansen, J.2
  • 68
    • 0002097632 scopus 로고
    • Versal normal form computation and representation theory
    • Tournier E. (Ed), Cambridge Univ. Press, Cambridge
    • Sanders J.A. Versal normal form computation and representation theory. In: Tournier E. (Ed). Computer Algebra and Differential Equations (1994), Cambridge Univ. Press, Cambridge 185-210
    • (1994) Computer Algebra and Differential Equations , pp. 185-210
    • Sanders, J.A.1
  • 69
    • 0003567524 scopus 로고
    • Verzweigungstheorie homokliner Verdopplungen
    • University of Stuttgart, Germany
    • Sandstede B. Verzweigungstheorie homokliner Verdopplungen. Ph.D. thesis (1993), University of Stuttgart, Germany
    • (1993) Ph.D. thesis
    • Sandstede, B.1
  • 70
    • 0031485993 scopus 로고    scopus 로고
    • Convergence estimates for the numerical approximation of homoclinic solutions
    • Sandstede B. Convergence estimates for the numerical approximation of homoclinic solutions. IMA J. Numer. Anal. 17 (1997) 437-462
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 437-462
    • Sandstede, B.1
  • 71
    • 0027641608 scopus 로고
    • Numerical computation of saddle-node homoclinic bifurcation points
    • Schecter S. Numerical computation of saddle-node homoclinic bifurcation points. SIAM J. Numer. Anal. 30 (1993) 1155-1178
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1155-1178
    • Schecter, S.1
  • 72
    • 21844510897 scopus 로고
    • Rate of convergence of numerical approximations to homoclinic bifurcation points
    • Schecter S. Rate of convergence of numerical approximations to homoclinic bifurcation points. IMA J. Numer. Anal. 15 (1995) 23-60
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 23-60
    • Schecter, S.1
  • 74
  • 75
    • 0008525582 scopus 로고
    • Sur une extension du calcul des substitutions linéares
    • Stéphanos C. Sur une extension du calcul des substitutions linéares. J. Math. Pures Appl. 6 (1900) 73-128
    • (1900) J. Math. Pures Appl. , vol.6 , pp. 73-128
    • Stéphanos, C.1
  • 77
    • 0000595530 scopus 로고    scopus 로고
    • Computation of Hopf bifurcations with bordered matrices
    • Werner B. Computation of Hopf bifurcations with bordered matrices. SIAM J. Numer. Anal. 33 (1996) 435-455
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 435-455
    • Werner, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.