fractal (version 2.0-4)

henon: Henon map

Description

Calculates the Henon map states using the specifed parameter set. The Henon map is defined as $$ x_n = a - x_{n - 1}^2 + b y_{n - 1}$$ $$ y_n = x_{n - 1}$$

A parameter set of \(a=1.4\) and \(b=0.3\) is known to produce a deterministic chaotic response.

Usage

henon(start=rnorm(2), a=1.4, b=0.3, n.sample=2000, n.transient=10)

Arguments

start

a two-element vector of numeric values denoting the starting values for the X and Y Henon coordinates, respectively.

a

the a parameter. Default: 1.4.

b

the b parameter. Default: 0.3.

n.sample

an integer denoting the number of iterates to create beyond that specified by n.transient. Default: 2000.

n.transient

an integer denoting the number of transient points. These transients are removed from the output. Default: 10.

Value

a list of vectors named x and y corresponding to the X- and Y states of the Henon map, respectively.

See Also

lorenz, lorenz.ode.

Examples

# NOT RUN {
plot(henon(),pch=".",cex=0.1)
# }