Sinai map
Generates a 2-dimensional time series using the Sinai map.
sinaiMap( a = 0.1, start = runif(2), n.sample = 5000, n.transient = 500, do.plot = TRUE )
a |
The a parameter. Default: 0.1 |
start |
A 2-dimensional vector indicating the starting values for the x and y Sinai 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 Sinai system is shown. |
The Sinai map is defined as follows:
x[n+1] = (x[n] + y[n] + a*cos(2*pi*y[n]) )mod 1
y[n+1] = (x[n] + 2*y[n])mod 1
The default selection for the a parameter 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 Sinai map, respectively.
Some initial values may lead to an unstable system that will tend to infinity.
Constantino A. Garcia
Mcsharry, P. E. and P. R. Ruffino (2003). Asymptotic angular stability in nonlinear systems: rotation numbers and winding numbers. Dynamical Systems 18(3), 191-200.
## Not run: sinai.map = sinaiMap(n.sample = 1000, n.transient=10,do.plot=TRUE) # accessing the x coordinate and plotting it plot(ts(sinai.map$x)) ## End(Not run)
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