Fold and Homoclinic bifurcation

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I have a question of the positioning of bifurcation lines in 2D-parameterspace.



say we have a system of ODE's with two bifurcation parameters.



My understanding of the bifurcation lines is that the Fold line should contain the Homoclinic, and that they only tangentially meet in a Takens Bogdanov bifurcation point, but don't cross.



Is this true?







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    up vote
    0
    down vote

    favorite












    I have a question of the positioning of bifurcation lines in 2D-parameterspace.



    say we have a system of ODE's with two bifurcation parameters.



    My understanding of the bifurcation lines is that the Fold line should contain the Homoclinic, and that they only tangentially meet in a Takens Bogdanov bifurcation point, but don't cross.



    Is this true?







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I have a question of the positioning of bifurcation lines in 2D-parameterspace.



      say we have a system of ODE's with two bifurcation parameters.



      My understanding of the bifurcation lines is that the Fold line should contain the Homoclinic, and that they only tangentially meet in a Takens Bogdanov bifurcation point, but don't cross.



      Is this true?







      share|cite|improve this question














      I have a question of the positioning of bifurcation lines in 2D-parameterspace.



      say we have a system of ODE's with two bifurcation parameters.



      My understanding of the bifurcation lines is that the Fold line should contain the Homoclinic, and that they only tangentially meet in a Takens Bogdanov bifurcation point, but don't cross.



      Is this true?









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 21 at 16:17









      John Ma

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      37.7k93669










      asked Aug 20 at 13:02









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