NUMERICAL COMPUTATION OF SADDLE-NODE HOMOCLINIC BIFURCATION POINTS

In two-parameter families of vector fields there can be curves in the parameter plane along which orbits homoclinic to hyperbolic equilibria occur. Such curves can end at a point where there is an orbit homoclinic to an equilibrium undergoing saddle-node or transcritical bifurcation. Convergence and stability results are presented for a method of approximating these special parameter values and their associated homoclinic orbits.