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- W2089075214 abstract "In the logistic map, the simplest of stable odd-numbered cycles is a 3-cycle. It comes into existence after the stable 2k cycles cease to exist. The 3-cycle is thus important as a route to chaos. In 1977 Guckenheimer et al. [J. Math. Biol. 4, 101 (1977)] first estimated the value of the control parameter a at which it can be superstable. It implies that a stable 3-cycle can be formed and deformed at some values of a straddling that of the superstable 3-cycle. In this work we present an exact value of a for the superstable 3-cycle by reducing a polynomial of degree 7 to that of 3. The relevance of this work to Sharkovskii’s theorem is also discussed." @default.
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- W2089075214 date "2009-12-01" @default.
- W2089075214 modified "2023-10-17" @default.
- W2089075214 title "Analytical study of the superstable 3-cycle in the logistic map" @default.
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- W2089075214 doi "https://doi.org/10.1063/1.3266875" @default.
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