How to Achieve This?

In this section some of the steps to follow will be enumarated. those steps are the guide in our serch. Advances on each step are presented on the "What is done" section.

 

• Build a long time series using a given dynamical system and Runge-Kutta algorithm as an aporximation to the real flow.

• To get a map from the flow using a Poincare section.

• Search for close returns after n crossings. Here n is the period of the orbit we are trying to find.

• Select all the points who has a close return after n crossings and separate them on groups (clusters). This is necesary because there will be k UPOs with the same period!!!

• Once a cluster is defined it is time to average all the points in the cluster. We expect the center of mass to be a good approximation to a point over the periodic orbit. It has been reported that the precision of this aproximatimation grows as the squre root of the number of points (REFERENCE).

• Use RK algorithm with the found point as initial condition to get the trajectory (A closed one we expect!!!).

• Build the recurrence plots for this UPO and apply some other time series analysis technics to it.

• Compare the UPOs' recurrence plots to the recurrence plot we get from a trajectory on the attractor.