Threshold and Attractor diameter

General discussions and questions about recurrence plot and recurrence network related methods.
saravana
Junior
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Joined: Sat Jun 18, 2016 16:45
Affiliation (Univ., Inst., Dept.): IIT-Bombay
Location: powai,Mumbai, India
Research field: Combustion dynamics

Threshold and Attractor diameter

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
Expert
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Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

Re: Threshold and Attractor diameter

(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):

Code: Select all

``````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).