cliffordMap {nonlinearTseries}

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()
)

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.

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.

Value

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

Note

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

Author(s)

Constantino A. Garcia

See Also

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

Examples

## 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)