nonlinearTseries (version 0.3.1)

sinaiMap: 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()
)

Value

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

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.

Author

Constantino A. Garcia

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.

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

if (FALSE) {
sinai.map = sinaiMap(n.sample = 1000, n.transient=10,do.plot=TRUE)
# accessing the x coordinate and plotting it
plot(ts(sinai.map$x))
}