메뉴 건너뛰기




Volumn 11, Issue 4, 1996, Pages 325-346

Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; MATHEMATICAL MODELS; NUMERICAL METHODS;

EID: 0030405090     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119608806230     Document Type: Article
Times cited : (11)

References (33)
  • 1
    • 0016619787 scopus 로고
    • Qualitative investigation of a particular nonlinear system
    • Bautin, A. (1975) Qualitative investigation of a particular nonlinear system. Applied Mathematical Mechanics 39, 606-615.
    • (1975) Applied Mathematical Mechanics , vol.39 , pp. 606-615
    • Bautin, A.1
  • 2
    • 3042990034 scopus 로고
    • On the nonlocal application of the method of small parameter
    • Bautin, A. (1977) On the nonlocal application of the method of small parameter. Applied Mathematical Mechanics 41, 910-919.
    • (1977) Applied Mathematical Mechanics , vol.41 , pp. 910-919
    • Bautin, A.1
  • 3
    • 0002433039 scopus 로고
    • Global bifurcations and their numerical computation
    • eds D. Roose, A. Spence and B. De Dier; Kluwer, Dordrecht, Netherlands
    • Beyn, W.-J. (1990a) Global bifurcations and their numerical computation. Continuation and Bifurcations: Numerical Techniques and Applications (eds D. Roose, A. Spence and B. De Dier; Kluwer, Dordrecht, Netherlands), pp. 169-181.
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 169-181
    • Beyn, W.-J.1
  • 4
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • Beyn, W.-J. (1990b) The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis 9, 379-405.
    • (1990) IMA Journal of Numerical Analysis , vol.9 , pp. 379-405
    • Beyn, W.-J.1
  • 5
    • 21844504535 scopus 로고
    • Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point
    • Beyn, W.-J. (1994) Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis 14, 381-410.
    • (1994) IMA Journal of Numerical Analysis , vol.14 , pp. 381-410
    • Beyn, W.-J.1
  • 6
    • 0041967189 scopus 로고
    • On one simple model of kinetic self-oscillations in catalytic reaction of CO oxidation
    • Bykov, V., Yablonski, G. and Kim, V. (1978) On one simple model of kinetic self-oscillations in catalytic reaction of CO oxidation. Soviet Mathematics Doklady 19, 637-639.
    • (1978) Soviet Mathematics Doklady , vol.19 , pp. 637-639
    • Bykov, V.1    Yablonski, G.2    Kim, V.3
  • 8
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homoclinic bifurcations
    • Champneys, A. and Kuznetsov, Y. (1994) Numerical detection and continuation of codimension-two homoclinic bifurcations. International Journal of Bifurcation and Chaos 4, 785-822.
    • (1994) International Journal of Bifurcation and Chaos , vol.4 , pp. 785-822
    • Champneys, A.1    Kuznetsov, Y.2
  • 9
    • 0003834782 scopus 로고
    • HOMCONT: An AUTO86 driver for homoclinic bifurcation analysis
    • Version 2.0, CWI, Amsterdam. Report AM-R9516
    • Champneys, A., Kuznetsov, Y. and Sandstede, B. (1995) HOMCONT: An AUTO86 driver for homoclinic bifurcation analysis. Version 2.0, technical report, CWI, Amsterdam. Report AM-R9516.
    • (1995) Technical Report
    • Champneys, A.1    Kuznetsov, Y.2    Sandstede, B.3
  • 13
    • 0000025015 scopus 로고
    • Homoclinic bifurcations with nonhyperbolic equilibria
    • Deng, B. (1990) Homoclinic bifurcations with nonhyperbolic equilibria. SIAM Journal of Mathematical Analysis 21, 693-720.
    • (1990) SIAM Journal of Mathematical Analysis , vol.21 , pp. 693-720
    • Deng, B.1
  • 14
    • 0001755071 scopus 로고
    • AUTO, a program for the automatic bifurcation analysis of autonomous systems
    • Doedel, E. (1981) AUTO, a program for the automatic bifurcation analysis of autonomous systems. Congressus Numerantium 30, 265-384.
    • (1981) Congressus Numerantium , vol.30 , pp. 265-384
    • Doedel, E.1
  • 15
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems: (I) Bifurcation in finite dimensions
    • Doedel, E., Keller, H. and Kernévez, J. (1991a) Numerical analysis and control of bifurcation problems: (I) Bifurcation in finite dimensions. International Journal of Bifurcation and Chaos 1, 493-520.
    • (1991) International Journal of Bifurcation and Chaos , vol.1 , pp. 493-520
    • Doedel, E.1    Keller, H.2    Kernévez, J.3
  • 16
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems: (II) Bifurcation in infinite dimensions
    • Doedel, E., Keller, H. and Kernévez, J. (1991b) Numerical analysis and control of bifurcation problems: (II) Bifurcation in infinite dimensions. International Journal of Bifurcation and Chaos 1, 745-772.
    • (1991) International Journal of Bifurcation and Chaos , vol.1 , pp. 745-772
    • Doedel, E.1    Keller, H.2    Kernévez, J.3
  • 17
    • 0004057181 scopus 로고
    • On locating homoclinic and heteroclinic orbits
    • Cornell Theory Center, Center for Applied Mathematics, Cornell University
    • Doedel, E., Friedman, M. and Monteiro, A. (1993) On locating homoclinic and heteroclinic orbits. Technical report, Cornell Theory Center, Center for Applied Mathematics, Cornell University.
    • (1993) Technical Report
    • Doedel, E.1    Friedman, M.2    Monteiro, A.3
  • 18
    • 0000162712 scopus 로고
    • Cubic Liénard equations with linear damping
    • Dumortier, F. and Rousseau, C. (1990) Cubic Liénard equations with linear damping. Nonlinearity 3, 1015-1039.
    • (1990) Nonlinearity , vol.3 , pp. 1015-1039
    • Dumortier, F.1    Rousseau, C.2
  • 19
    • 0011311010 scopus 로고
    • Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds
    • Friedman, M. (1993) Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds. Journal of Dynamic Differential Equations 5, 59-87.
    • (1993) Journal of Dynamic Differential Equations , vol.5 , pp. 59-87
    • Friedman, M.1
  • 20
    • 0026170304 scopus 로고
    • Numerical computation and continuation of invariant manifolds connecting fixed points
    • Friedman, M. and Doedel, E. (1991) Numerical computation and continuation of invariant manifolds connecting fixed points. SIAM Journal of Numerical Analysis 28, 789-808.
    • (1991) SIAM Journal of Numerical Analysis , vol.28 , pp. 789-808
    • Friedman, M.1    Doedel, E.2
  • 21
    • 2042442839 scopus 로고
    • Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study
    • Friedman, M. and Doedel, E. (1993) Computational methods for global analysis of homoclinic and heteroclinic orbits: a case study. Journal of Dynamic Differential Equations 5, 37-57.
    • (1993) Journal of Dynamic Differential Equations , vol.5 , pp. 37-57
    • Friedman, M.1    Doedel, E.2
  • 23
    • 0003324839 scopus 로고
    • Global bifurcations in flows
    • eds T. Bedford and J. Swift; Cambridge University Press, Cambridge
    • Glendinning, P. (1988) Global bifurcations in flows. New Directions Dynamical Systems (eds T. Bedford and J. Swift; Cambridge University Press, Cambridge).
    • (1988) New Directions Dynamical Systems
    • Glendinning, P.1
  • 24
    • 21344489751 scopus 로고
    • Travelling waves with spatially resonant forcing: Bifurcations of a modified Landau equation
    • Glendinning, P. and Proctor, M. (1993) Travelling waves with spatially resonant forcing: bifurcations of a modified Landau equation. International Journal of Bifurcation and Chaos 3, 1447-1455.
    • (1993) International Journal of Bifurcation and Chaos , vol.3 , pp. 1447-1455
    • Glendinning, P.1    Proctor, M.2
  • 25
    • 0010757571 scopus 로고
    • Homoclinic orbits in a simple chemical model of an autocatalytic reaction
    • Kaas-Peterson, C. and Scott, S. (1988) Homoclinic orbits in a simple chemical model of an autocatalytic reaction. Physica D 32, 461-470.
    • (1988) Physica D , vol.32 , pp. 461-470
    • Kaas-Peterson, C.1    Scott, S.2
  • 26
    • 0003316491 scopus 로고
    • LINBIF: A program for continuation and bifurcation analysis of equilibria up to codimension three
    • eds D. Roose, A. Spence and B. De Dier; Kluwer, Dordrecht, Netherlands
    • Khibnik, A. (1990) LINBIF: a program for continuation and bifurcation analysis of equilibria up to codimension three. Continuation and Bifurcations: Numerical Techniques and Applications (eds D. Roose, A. Spence and B. De Dier; Kluwer, Dordrecht, Netherlands), pp. 283-296.
    • (1990) Continuation and Bifurcations: Numerical Techniques and Applications , pp. 283-296
    • Khibnik, A.1
  • 27
    • 0001028637 scopus 로고
    • Bifurcations of dynamical systems with a saddle-point separatrix loop
    • Lukyanov, V. (1982) Bifurcations of dynamical systems with a saddle-point separatrix loop. Differential Equations 18, 1049-1059.
    • (1982) Differential Equations , vol.18 , pp. 1049-1059
    • Lukyanov, V.1
  • 28
    • 3042994977 scopus 로고    scopus 로고
    • Convergence estimates for the numerical approximation of homoclinic solutions
    • in press
    • Sandstede, B. (1996) Convergence estimates for the numerical approximation of homoclinic solutions. IMA Journal of Numerical Analysis (in press).
    • (1996) IMA Journal of Numerical Analysis
    • Sandstede, B.1
  • 29
    • 0001449766 scopus 로고
    • The saddle-node separatrix-loop bifurcation
    • Schecter, S. (1987) The saddle-node separatrix-loop bifurcation. SIAM Journal of Applied Mathematics 18, 1142-1157.
    • (1987) SIAM Journal of Applied Mathematics , vol.18 , pp. 1142-1157
    • Schecter, S.1
  • 30
    • 0027641608 scopus 로고
    • Numerical computation of saddle-node homoclinic bifurcation points
    • Schecter, S. (1993) Numerical computation of saddle-node homoclinic bifurcation points. SIAM Journal of Numerical Analysis 30, 1155-1178.
    • (1993) SIAM Journal of Numerical Analysis , vol.30 , pp. 1155-1178
    • Schecter, S.1
  • 31
    • 21844510897 scopus 로고
    • Rate of convergence of numerical approximations to homoclinic bifurcation points
    • Schecter, S. (1995) Rate of convergence of numerical approximations to homoclinic bifurcation points. IMA Journal of Numerical Analysis 15, 23-60.
    • (1995) IMA Journal of Numerical Analysis , vol.15 , pp. 23-60
    • Schecter, S.1
  • 32
    • 0000851724 scopus 로고
    • On a new type of bifurcation of multidimensional dynamical systems
    • Shil'nikov, L. (1969) On a new type of bifurcation of multidimensional dynamical systems. Soviet Mathematics Doklady 10, 1368-1371.
    • (1969) Soviet Mathematics Doklady , vol.10 , pp. 1368-1371
    • Shil'nikov, L.1
  • 33
    • 0000980419 scopus 로고
    • On bifurcations of homoclinic 'figure eight' from a saddle with a negative saddle value
    • Turaev, D. and Shil'nikov, L. (1987) On bifurcations of homoclinic 'figure eight' from a saddle with a negative saddle value. Soviet Mathematics Doklady 34, 397-401.
    • (1987) Soviet Mathematics Doklady , vol.34 , pp. 397-401
    • Turaev, D.1    Shil'nikov, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.