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    Recurrence Plot

    Definition

    A recurrence plot is defined as a plot of the quantity R(t, τ) = H(ε - left double bracketing bar f(t) - f(τ) right double bracketing bar ), where H(x) is the Heaviside step function and left double bracketing bar f right double bracketing bar denotes a norm. A recurrence plot is therefore a binary plot. The figure above shows a recurrence plot for the Lorenz attractor with r = 28, σ = 10, b = 8/3, x(0) = 1, y(0) = 0, z(0) = 0, and ϵ = 5. Recurrence plots were initially used to graphically display nonstationarity in time series (Eckmann et al. 1987, Gao and Cai 2000), but are also useful for visualizing functions.

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