PERIOD-DOUBLING BIFURCATION 2)
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A threshold in a process that tends to turn chaotic, signaled by the replacement of a period n cycle by a period 2n cycle.
After such a bifurcation the repetition of a certain state of the system needs twice the number of time-steps. When repeated time and again these events are akin to a fractalization of the cycles.
In the case of the logistic equation, as stated by R. JENSEN: "The range of (the parameter) a over which a single cycle is stable decreases rapidly as the period of the cycle increases, which accounts for the rapid accumulation of cycles with larger and larger periods" (1987, p.171).
For a ≥ 3,57 the global cycle's period becomes infinite.
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Bertalanffy Center for the Study of Systems Science(2020).
To cite this page, please use the following information:
Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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