Invariant manifolds of the Bonhoeffer-van der Pol oscillator

Details Invariant manifolds of the Bonhoeffer-van der Pol oscillator Invariant manifolds of the Bonhoeffer-van der Pol oscillator

2010-07-20

arxiv.org/abs/1007.3375v1

Chaos Solitons Fractals. 40 (2009), 2170-2180

Nonlinear Sciences

Chaotic Dynamics

14 pages, 15 figures

Scientific paper

10.1016/j.chaos.2007.10.018

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 (whic 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.

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