Exotic Homoclinic Surface of a Saddle-Node Limit Cycle in a Leech Neuron Model

We carry out numerical and theoretical investigations on the global unstable invariant set (manifold) of a saddle-node limit cycle in a leech heart interneuron model. The corresponding global bifurcation is accompanied by an explosion of secondary bifurcations of limit cycles and the emergence of loop-shaped bifurcation structures. The dynamical behaviors of the trajectories of the invariant set are very complicated and can only be partially explained by existing theories.