Threshold and Attractor diameter

[saravana]

In the CRP toolbox, for detecting the neighbors/recurrence I know that you have to specify a threshold. What does this threshold represent in the toolbox? For e.g. one example given in the manual says threshold is 6%. Is this 6% of attractor diameter or some other non-dimensional distance? How do I calculate the attractor diameter?

[Norbert]

(reply refers to the CRP Toolbox)
It depends on the selected recurrence criterion. When it is a fixed size of the neighbourhood, such for EUC, MAX, MIN, then it is the absolute value of ε. But there are also "dynamical thresholds", such as selecting the fixed amount of nearest neighbours (FAN) or fixed recurrence rate (RR). The value you can enter is then just the final RR value, e.g. 0.06 (i.e. 6%).

If you prefer to use a fixed size of the neighbourhood and relate ε to the phase space diameter, then you can also use a fraction. But the threshold is then different. In the CRP Toolbox you can calculate the phase space diameter with the function pss (pss in the CRP Toolbox):

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maxDiam = pss(x,m,tau);
epsilon = 0.1 * maxDiam

(here m and tau are the embedding parameters and epsilon would be 10% of the max. phase space diameter).

Look also at my reply on topic radius threshold.