arXiv 1007.33752010-07-20nlin.CDmath.DS

Invariant manifolds of the Bonhoeffer-van der Pol oscillator

R. Benítez, V. J. Bolós

备注：: 14 pages, 15 figures
发表信息：: Chaos Solitons Fractals. 40 (2009), 2170-2180
DOI：: 10.1016/j.chaos.2007.10.018

英文摘要：

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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