henon: Henon map

In nonlinearTseries: Nonlinear Time Series Analysis

Henon map

Description

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

Usage

henon(
  start = runif(min = -0.5, max = 0.5, n = 2),
  a = 1.4,
  b = 0.3,
  n.sample = 5000,
  n.transient = 500,
  do.plot = deprecated()
)

Arguments

start	A 2-dimensional vector indicating the starting values for the x and y Henon coordinates. If the starting point is not specified, it is generated randomly.
a	The a parameter. Default: 1.4.
b	The b parameter. Default: 0.3.
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 Henon system is shown. Before version 0.2.11, default value was TRUE; versions 0.2.11 and later use FALSE as default.

Details

The Henon map is defined as follows:

x_n = 1 - a \cdot x_{n - 1}^2 + y_{n - 1}

y_n = b \cdot x_{n - 1}

The default selection for both a and b parameters (a=1.4 and b=0.3) 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 Henon map, respectively.

Note

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

Author(s)

Constantino A. Garcia

References

Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)

See Also

logisticMap, lorenz, rossler, ikedaMap, cliffordMap, sinaiMap, gaussMap

Examples

## Not run: 
henon.map=henon(n.sample = 1000, n.transient=10,do.plot=TRUE,
               start=c(-0.006423277,-0.473545134))
# accessing the x coordinate and plotting it
plot(ts(henon.map$x))

## End(Not run)

nonlinearTseries documentation built on Sept. 23, 2024, 5:10 p.m.