poincareMap: Poincare map

Description Usage Arguments Details Value Author(s) References Examples

View source: R/poincareMap.R

Description

Computes the Poincare map of the reconstructed trajectories in the phase-space.

The Poincare map is a classical dynamical system technique that replaces the n-th dimensional trajectory in the phase space with an (n-1)-th order discrete-time called the Poincare map. The points of the Poincare map are the intersection of the trajectories in the phase-space with a certain Hyper-plane.

Usage

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poincareMap(time.series = NULL, embedding.dim = 2, time.lag = 1,
  takens = NULL, normal.hiperplane.vector = NULL, hiperplane.point)

Arguments

time.series

The original time series from which the phase-space reconstruction is done.

embedding.dim

Integer denoting the dimension in which we shall embed the time.series.

time.lag

Integer denoting the number of time steps that will be use to construct the Takens' vectors.

takens

Instead of specifying the time.series, the embedding.dim and the time.lag, the user may specify directly the Takens' vectors.

normal.hiperplane.vector

The normal vector of the hyperplane that will be used to compute the Poincare map. If the vector is not specifyed the program choses the vector (0,0,...,1).

hiperplane.point

A point on the hyperplane (an hyperplane is defined with a point and a normal vector).

Details

This function computes the Poincare map taking the Takens' vectors as the continuous trajectory in the phase space. The takens param has been included so that the user may specify the real phase-space instead of using the phase-space reconstruction (see examples).

Value

Since there are three different Poincare maps, an R list is returned storing all the information related which all of these maps:

Author(s)

Constantino A. Garcia

References

Parker, T. S., L. O. Chua, and T. S. Parker (1989). Practical numerical algorithms for chaotic systems. Springer New York

Examples

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## Not run: 
r=rossler(a = 0.2, b = 0.2, w = 5.7, start=c(-2, -10, 0.2),
time=seq(0,300,by = 0.01), do.plot=FALSE)
takens=cbind(r$x,r$y,r$z)
# calculate poincare sections
pm=poincareMap(takens = takens,normal.hiperplane.vector = c(0,1,0), 
 hiperplane.point=c(0,0,0) )
plot3d(takens,size=0.7)
points3d(pm$pm,col="red")
## End(Not run)

nonlinearTseries documentation built on Sept. 23, 2018, 9:03 a.m.