Wada boundary bifurcations induced by boundary saddle–saddle collision

Abstract

In this letter, a Wada boundary bifurcation (WBB) induced by a boundary saddle touching another boundary saddle is first found through the study of a forced damped pendulum. The WBB can be quantitatively described by the change both in the number of basins involved and in the geometrical size of the boundary. We perceive the manifold structures of the two saddles, that is, a pre-existence of heteroclinic crossing and the other nearly forming heteroclinic tangency exist before the WBB. So we schematically construct the equivalent topological structure of the manifolds of arbitrary two saddles, and rigorously prove two theorems that indicate the existence of the heteroclinic tangency and thus generically confirm the mechanism of such WBB.