Abstract
CASCADES OF period-doubling bifurcations have been seen in the great majority of low-dimensional systems that exhibit chaotic behavior. A “cascade” appears as an infinite sequence of period-doubling bifurcations. A stable periodic orbit is seen to become unstable as a parameter is increased or decreased and is replaced by a stable periodic orbit of twice its period. This orbit in turn becomes unstable and is replaced by a new stable orbit with its period again doubled, and the process continues through an infinity of such period-doubling bifurcations.KeywordsPeriodic OrbitBifurcation DiagramPeriodic PointChaotic AttractorStable OrbitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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