Constructing dynamical systems having homoclinic bifurcation points of codimension two

  • Björn Sandstede


A procedure is derived which allows for a systematic construction of three-dimensional ordinary differential equations having homoclinic solutions. The equations are proved to exhibit codimension-two homoclinic bifurcation points. Examples include the non-orientable resonant bifurcation, the inclination-flip, and the orbit-flip. In addition, an equation is constructed which has a homoclinic orbit converging to a saddle-focus satisfying Shilnikov's condition. The vector fields are polynomial and non-stiff in that the eigenvalues are of moderate size.

Key words

Homoclinic orbits bifurcations 

AMS subject classifications

34C37 58F14 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Björn Sandstede
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidence

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