A HOMOCLINIC HIERARCHY

Homoclinic bifurcations in autonomous ordinary differential equations provide useful organizing centres for the analysis of examples. There are four generic types of homoclinic bifurcation, depending on the dom inant eigenvalues of the Jacobian matrix of the flow near a stationary point. A family of differential equations is presented which, for sui table choices of parameters, can exhibit each of these four homoclinic bifurcations. Ln one of the cases this provides the first smooth exam ple of the bifurcation in the literature.