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Volumn 38, Issue 3, 2012, Pages

Interactive initialization and continuation of homoclinic and heteroclinic orbits in MATLAB

Author keywords

Global bifurcation; Homotopy; Numerical continuation

Indexed keywords

CODIMENSION-TWO; CONTINUATION OF INVARIANT SUBSPACES; EQUILIBRIUM POINT; GLOBAL BIFURCATIONS; HETEROCLINIC ORBIT; HOMOCLINIC; HOMOCLINIC BIFURCATIONS; HOMOCLINIC ORBITS; HOMOTOPIES; HOMOTOPY METHOD; HOPF POINT; KEY FEATURE; LIMIT CYCLE; LIMIT POINTS; NUMERICAL CONTINUATION; NUMERICAL STUDIES; PARAMETERIZED; TEST FUNCTIONS; TORUS BIFURCATION;

EID: 84862073931     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/2168773.2168776     Document Type: Article
Times cited : (37)

References (30)
  • 2
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • BEYN, W. J. 1990. The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Anal. 10, 3, 379-405.
    • (1990) IMA J. Numer. Anal. , vol.10 , Issue.3 , pp. 379-405
    • Beyn, W.J.1
  • 4
    • 0038228324 scopus 로고    scopus 로고
    • Numerical continuation, and computation of normal forms
    • B. Fiedler Ed. Elsevier Science, North Holland, Amsterdam
    • BEYN, W. J., CHAMPNEYS, A., DOEDEL, E., GOVAERTS, W., KUZNETSOV, YU. A., AND SANDSTEDE, B. 2002. Numerical continuation, and computation of normal forms. In Handbook of Dynamical Systems, B. Fiedler Ed., Vol. 2. Elsevier Science, North Holland, Amsterdam, 149-219.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 149-219
    • Beyn, W.J.1    Champneys, A.2    Doedel, E.3    Govaerts, W.4    Kuznetsov, Y.U.A.5    Sandstede, B.6
  • 5
    • 55549112582 scopus 로고    scopus 로고
    • Continuation of invariant subspaces in large scale bifurcation problems
    • BINDEL, D., DEMMEL, J., AND FRIEDMAN, M. 2008. Continuation of invariant subspaces in large scale bifurcation problems. SIAM J. Sci. Comput. 30, 2, 637-656.
    • (2008) SIAM J. Sci. Comput. , vol.30 , Issue.2 , pp. 637-656
    • Bindel, D.1    Demmel, J.2    Friedman, M.3
  • 6
    • 0011317221 scopus 로고
    • On the structure of a neighborhood of a separatrix contour with a saddle-focus
    • Gorkii State University, Gorkii In Russian
    • BYKOV, V. V. 1978. On the structure of a neighborhood of a separatrix contour with a saddle-focus. In Methods of Qualitative Theory of Differential Equations, Gorkii State University, Gorkii, 3-32 (In Russian).
    • (1978) Methods of Qualitative Theory of Differential Equations , pp. 3-32
    • Bykov, V.V.1
  • 7
    • 0011355649 scopus 로고
    • Bifurcations of dynamical systems close to systems with a separatrix contour containing a saddle-focus
    • Gorkii State University, Gorkii In Russian
    • BYKOV, V. V. 1980. Bifurcations of dynamical systems close to systems with a separatrix contour containing a saddle-focus. In Methods of Qualitative Theory of Differential Equations, Gorkii State University, Gorkii, 44-72 (In Russian).
    • (1980) Methods of Qualitative Theory of Differential Equations , pp. 44-72
    • Bykov, V.V.1
  • 8
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homoclinic bifurcations
    • CHAMPNEYS, A. R. AND KUZNETSOV, YU. A. 1994. Numerical detection and continuation of codimension-two homoclinic bifurcations. Int. J. Bifur. Chaos Appl. Sci. Eng. 4, 4, 785-822.
    • (1994) Int. J. Bifur. Chaos Appl. Sci. Eng. , vol.4 , Issue.4 , pp. 785-822
    • Champneys, A.R.1    Kuznetsov, Y.U.A.2
  • 10
    • 0034456294 scopus 로고    scopus 로고
    • Computing connecting orbits via an improved algorithm for continuing invariant subspaces
    • DOI 10.1137/S1064827598344868, PII S1064827598344868
    • DEMMEL, J. W., DIECI, L., AND FRIEDMAN, M. J. 2000. Computing connecting orbits via an improved algorithm for continuing invariant subspaces. SIAM J. Sci. Comput. 22, 1, 81-94. (Pubitemid 32270872)
    • (2000) SIAM Journal of Scientific Computing , vol.22 , Issue.1 , pp. 81-94
    • Demmel, J.W.1    Dieci, L.2    Friedman, M.J.3
  • 11
    • 8744230577 scopus 로고    scopus 로고
    • MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
    • DOI 10.1145/779359.779362
    • DHOOGE, A., GOVAERTS, W., AND KUZNETSOV, YU. A. 2003. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29, 2, 141-164. (Pubitemid 40001448)
    • (2003) ACM Transactions on Mathematical Software , vol.29 , Issue.2 , pp. 141-164
    • Dhooge, A.1    Govaerts, W.2    Kuznetsov, Yu.A.3
  • 14
    • 0001058067 scopus 로고
    • Numerical computation of heteroclinic orbits
    • DOEDEL, E. J. AND FRIEDMAN, M. J. 1989. Numerical computation of heteroclinic orbits. J. Comput. Appl. Math. 26, 1-2, 155-170.
    • (1989) J. Comput. Appl. Math. , vol.26 , Issue.1-2 , pp. 155-170
    • Doedel, E.J.1    Friedman, M.J.2
  • 17
    • 0031504868 scopus 로고    scopus 로고
    • Successive continuation for locating connecting orbits
    • DOEDEL, E. J., FRIEDMAN, M. J., AND KUNIN, B. I. 1997b. Successive continuation for locating connecting orbits. N u m e r. A l g o r. 1 4, 1-3, 103-124.
    • (1997) Numer. Algor. , vol.14 , Issue.1-3 , pp. 103-124
    • Doedel, E.J.1    Friedman, M.J.2    Kunin, B.I.3
  • 18
    • 25144468397 scopus 로고    scopus 로고
    • Continuation of homoclinic orbits in MATLAB
    • Computational Science - ICCS 2005: 5th International Conference, Proceedings
    • FRIEDMAN, M., GOVAERTS, W., KUZNETSOV, YU. A., AND SAUTOIS, B. 2005. Continuation of homoclinic orbits in MATLAB. In Proceedings of the 5th International Conference on Computational Science, V. S. et al. Ed. Springer Verlag Lecture Notes in Computer Science Series, vol. 3514, ICCS, Atlanta, GA, 263-270. (Pubitemid 41342807)
    • (2005) Lecture Notes in Computer Science , vol.3514 , Issue.1 , pp. 263-270
    • Friedman, M.1    Govaerts, W.2    Kuznetsov, Yu.A.3    Sautois, B.4
  • 20
    • 34250127220 scopus 로고
    • T-points: A codimension two heteroclinic bifurcation
    • GLENDINNING, P. AND SPARROW, C. 1986. T-points: A codimension two heteroclinic bifurcation. J. Stat. Phys. 43, 3-4, 479-488.
    • (1986) J. Stat. Phys. , vol.43 , Issue.3-4 , pp. 479-488
    • Glendinning, P.1    Sparrow, C.2
  • 27
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • LORENZ, E. N. 1963. Deterministic nonperiodic flow. J. Atmospher. Sci. 20, 2, 130-141.
    • (1963) J. Atmospher. Sci. , vol.20 , Issue.2 , pp. 130-141
    • Lorenz, E.N.1
  • 29
    • 0002453062 scopus 로고
    • Analysis of neural excitability and oscillations
    • C. Koch and I. Segev Eds., MIT Press, Cambridge, MA
    • RINZEL, J. AND ERMENTROUT, G. B. 1989. Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling: From Synapses to Networks, C. Koch and I. Segev Eds., MIT Press, Cambridge, MA, 135-169.
    • (1989) Methods in Neuronal Modeling: From Synapses to Networks , pp. 135-169
    • Rinzel, J.1    Ermentrout, G.B.2
  • 30
    • 0035926571 scopus 로고    scopus 로고
    • Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions
    • DOI 10.1006/jtbi.2001.2293
    • TYSON, J. J. AND NOVAK, B. 2001. Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210, 2, 249-263. (Pubitemid 32575064)
    • (2001) Journal of Theoretical Biology , vol.210 , Issue.2 , pp. 249-263
    • Tyson, J.J.1    Novak, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.