Threshold and Attractor diameter

 Junior
 Posts: 2
 Joined: Sat Jun 18, 2016 16:45
 Affiliation (Univ., Inst., Dept.): IITBombay
 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 nondimensional distance? How do I calculate the attractor diameter?
 Norbert
 Expert
 Posts: 194
 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):(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.
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
Look also at my reply on topic radius threshold.