WIAS Preprint No. 149, (1995)

Constructing dynamical systems possessing homoclinic bifurcation points of codimension two


  • Sandstede, Björn




A procedure is derived which allows for a systematic construction of three-dimensional ordinary differential equations possessing homoclinic solutions. These are proved to admit homoclinic bifurcation points of codimension two. The examples include the non-orientable resonant bifurcation, the inclination-flip and the orbit-flip. In addition, an equation is constructed which admits 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.

Appeared in

  • J. Dynamics Differential Equations, 9 (1997), pp. 269-288

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