Attractor reconstruction and calculation of the largest Lyapunov exponent (LyE) and sample entropy (SampEn). (A) The original angle time series and the time-delayed copies [x(i+ τ),...,x(i + (m-1)τ)] used for attractor reconstruction. (B) The attractors were composed of sets of m-dimensional vectors v(i) = [x(i), x(i+ τ),...,x(i + (m-1)τ)], with i = 1,...,N - (m-1)τ. The delay τ was obtained from the first minimum of the average mutual information function and the dimension m was selected where the percentage of the global false nearest neighbours approached zero. (C) The LyE algorithm tracked the divergence of nearest neighbours over time, focusing on a reference trajectory with a single nearest neighbour being followed and replaced when its separation L'(t
) from the reference trajectory becomes large. The new neighbour was chosen to minimize the replacement length L(t
) and the angular separation θ
. Once the reference trajectory has gone over the data sample, was estimated, with M the total number of replacement steps [14, 15]. (D) For the SampEn, the first step consisted in calculating , where j≠i ranges from 1 to N - mτ, and is the maximum difference between the scalar components of the vectors [v(i), v(j)]. The distance r was chosen as 0.2× standard deviation of x(i). The density was obtained afterwards. (E) The procedure was repeated for an (m+1)-dimensional attractor, by computing Φm+1(τ, r). Finally, the negative log likelihood of the conditional probability that two close vectors (within r) in a m-dimensional attractor remain close in a (m+1)-dimensional attractor was obtained as SampEn = -τ-1 log (Φm+1(τ, r)/Φm(τ, r)) .