Fig. 2

Illustration of topologically equivalent attractors and topologically equivalent position. The two attractors M _X and M _Y are reconstructed from the original system by lagged-coordinates of its components X and Y. These two reconstructed attractors are topological equivalent. There are two short time-series {P _i } and {Q _i }(i = 1, 2, ⋯) on these two topologically equivalent attractors, respectively. And we call two points as topologically equivalent position, taking P ₄ and Q ₄ for example, if and only if the relative distance from P ₄ and Q ₄ to any other points on their corresponding attractors are invariant