From networks of unstable attractors to heteroclinic switching.
نویسندگان
چکیده
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other's basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems.
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عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 78 6 Pt 2 شماره
صفحات -
تاریخ انتشار 2008