Henon map

Description

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

Usage

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  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 = TRUE)

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 (default value), a plot of the generated Henon system is shown.

Details

The Henon map is defined as follows:

x[n] = 1 - a*x[n - 1]^2 + y[n - 1]

y[n] = b*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

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## 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)