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. 2017 Feb 3;7:41951. doi: 10.1038/srep41951

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Copyright © 2017, The Author(s)

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The entropy growth rate H of a τ-order aggregate network as a function of the order τ for (a) White noise, 1/f noise, AR(3) model s_n = 0.8s_n−1 − 0.5s_n−2 + 0.7s_n−3 + ε_n (ε_n is generated from white noise), and the Hénon map: and (b) Chaotic time series (i.e., the Hénon map, the Ikeda Map: x_n+1 = 1 + 0.9 (x_ncost_n − y_nsint_n), y_n+1 = 0.9 (x_nsint_n − y_ncost_n), where , the logistic map: x_n+1 = 4x_n(1 − x_n), and the Rössler system: = −(y + z), = x + 0.2y, = 0.2 + z(x − 5.7)). Note that here we choose the partition N = 2500, 1600, 900, 100 for the Hénon map, the Ikeda Map, the logistic map, and the Rössler system, respectively. The entropy growth rate H as a function of the order τ for the Hénon map in chaotic regime for (c) different time delays l and for (d) quadratic and cubic nonlinear transformations of the phase space. The planar insets show the corresponding phase portraits.

Inline graphic — The entropy growth rate H of a τ-order aggregate network as a function of the order τ for (a) White noise, 1/f noise, AR(3) model s_n = 0.8s_n−1 − 0.5s_n−2 + 0.7s_n−3 + ε_n (ε_n is generated from white noise), and the Hénon map: and (b) Chaotic time series (i.e., the Hénon map, the Ikeda Map: x_n+1 = 1 + 0.9 (x_ncost_n − y_nsint_n), y_n+1 = 0.9 (x_nsint_n − y_ncost_n), where , the logistic map: x_n+1 = 4x_n(1 − x_n), and the Rössler system: = −(y + z), = x + 0.2y, = 0.2 + z(x − 5.7)). Note that here we choose the partition N = 2500, 1600, 900, 100 for the Hénon map, the Ikeda Map, the logistic map, and the Rössler system, respectively. The entropy growth rate H as a function of the order τ for the Hénon map in chaotic regime for (c) different time delays l and for (d) quadratic and cubic nonlinear transformations of the phase space. The planar insets show the corresponding phase portraits.