Clifford map
Generates a 2-dimensional time series using the Clifford map.
cliffordMap( a = -1.4, b = 1.6, cc = 1, d = 0.7, start = runif(2), n.sample = 5000, n.transient = 500, do.plot = TRUE )
a |
The a parameter. Default: -1.4 |
b |
The b parameter. Default: 1.6 |
cc |
The c parameter. Default: 1.0 |
d |
The d parameter. Default: 0.7 |
start |
a 2-dimensional vector indicating the starting values for the x and y Clifford coordinates. If the starting point is not specified, it is generated randomly. |
n.sample |
Length of the generated time series. Default: 5000 samples. |
n.transient |
Number of transient samples that will be discarded. Default: 500 samples. |
do.plot |
Logical value. If TRUE (default value), a plot of the generated Clifford system is shown. |
The Clifford map is defined as follows:
x[n+1] = sin(a*y[n]) + c*cos(a*x[n])
y[n+1] = sin(b*x[n] + d*cos(b*y[n])
The default selection for the a b c and d parameters is known to produce a deterministic chaotic time series.
A list with two vectors named x and y containing the x-components and the y-components of the Clifford map, respectively.
Some initial values may lead to an unstable system that will tend to infinity.
Constantino A. Garcia
## Not run: clifford.map=cliffordMap(n.sample = 1000, n.transient=10,do.plot=TRUE) # accessing the x coordinate and plotting it plot(ts(clifford.map$x)) ## End(Not run)
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