sinaiMap {nonlinearTseries}

Sinai map

Description

Generates a 2-dimensional time series using the Sinai map.

Usage

sinaiMap(
  a = 0.1,
  start = runif(2),
  n.sample = 5000,
  n.transient = 500,
  do.plot = deprecated()
)

Arguments

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, a plot of the generated Sinai system is shown. Before version 0.2.11, default value was TRUE; versions 0.2.11 and later use FALSE as default.

Details

The Sinai map is defined as follows:

x_{n+1} = (x_{n} + y_{n} + a \cdot cos(2 \cdot pi \cdot y_{n}) )mod 1

y_{n+1} = (x_{n} + 2 \cdot y_n)mod 1

The default selection for the a parameter is known to produce a deterministic chaotic time series.

Value

A list with two vectors named x and y containing the x-components and the y-components of the Sinai map, respectively.

Note

Some initial values may lead to an unstable system that will tend to infinity.

Author(s)

Constantino A. Garcia

References

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.

See Also

henon, logisticMap, lorenz, rossler, ikedaMap, cliffordMap, gaussMap

Examples

## 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)