nonlinearTseries (version 0.3.1)

cliffordMap: Clifford map

Description

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

Usage

cliffordMap(
  a = -1.4,
  b = 1.6,
  cc = 1,
  d = 0.7,
  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 Clifford map, respectively.

Arguments

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, a plot of the generated Clifford 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 Clifford map is defined as follows: $$x_{n+1} = sin(a \cdot y_n) + c \cdot cos(a \cdot x_n)$$ $$y_{n+1} = sin(b \cdot x_n) + d \cdot cos(b \cdot y_n)$$ The default selection for the a b c and d parameters is known to produce a deterministic chaotic time series.

See Also

henon, logisticMap, lorenz, rossler, ikedaMap, sinaiMap, gaussMap

Examples

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