Border-collision period-doubling scenario

Details Border-collision period-doubling scenario Border-collision period-doubling scenario

Aug 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phrve..70b6222a&link_type=abstract

Physical Review E, vol. 70, Issue 2, id. 026222

Nonlinear Sciences

Chaotic Dynamics

2

Low-Dimensional Chaos, Oscillations, Chaos, And Bifurcations, Chaotic Dynamics

Scientific paper

Using a one-dimensional dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, we investigate the border-collision period-doubling bifurcation scenario. In contrast to the classical period-doubling scenario, this scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border-collision bifurcation and a pitchfork bifurcation. The characteristic properties of this scenario, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors and noninvariant attractive sets, are investigated.

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