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- W2061158095 abstract "Xn+l = rXnO -Xn),(1) where 0 < x_ 1 and 0 < r < 4. In other words, given some starting number 0 < xl < 1, we generate a new number x2 by the rule x2 = rx1(1 x 1), and then repeat the process to generate x3 from x2, and so on. This equation has many virtues: 1) It is accessible. High school students can explore its patterns, as long as they have access to a hand calculator or a small computer. 2) It is exemplary. This single example illustrates many of the fundamental notions of nonlinear dynamics, such as equilibrium, stability, periodicity, chaos, bifurcations, and fractals. May [6] was the first to stress the pedagogical value of (1). 3) It is living mathematics. Most of the important discoveries about the logistic map are less than 20 years old. Certain aspects of (1) are still not understood rigorously, and are being pursued by a few of the finest living mathematicians. 4) It is relevant to science. Predictions derived from the logistic map have been verified in experiments on weakly turbulent fluids, oscillating chemical reactions, nonlinear electronic circuits, and a variety of other systems [8]." @default.
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- W2061158095 date "1995-02-01" @default.
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- W2061158095 title "The Birth of Period Three" @default.
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- W2061158095 doi "https://doi.org/10.1080/0025570x.1995.11996273" @default.
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