Numerical continuation of degenerate homoclinic orbits in planar systems

In this paper we develop numerical algorithms for the continuation of degen erate homoclinic connections in planar systems. We consider the case where the equilibrium point has zero trace and two cases of higher-order degenera cies. The method we propose is able to continue homoclinic connections of o rder up to codimension-four. Application of the algorithm to four examples supports its validity and demonstrates its usefulness.