Invariant manifolds of the Bonhoeffer–van der Pol oscillator

The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer–van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (which are related to the creation or destruction of Smale horseshoes) and the chaos observed in the bifurcation diagram is described. It is observed that in the non-chaotic zones of the bifurcation diagram, there may or may not be Smale horseshoes, but there are no homoclinic tangencies.