ikedaMap(
a = 0.85,
b = 0.9,
cc = 7.7,
k = 0.4,
start = runif(2),
n.sample = 5000,
n.transient = 500,
do.plot = deprecated()
)
Value
a list with 2 vectors named x and y the x-components
and the y-components of the Ikeda map, respectively.
Arguments
a
The a parameter. Default: 0.85.
b
The b parameter. Default: 0.9.
cc
The c parameter. Default: 7.7.
k
The k parameter. Default: 0.4.
start
a 2-dimensional numeric vector indicating the starting value for the time series.
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 ikeda 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 Ikeda map is defined as follows:
$$z_{n+1} = a + b \cdot z_n \cdot exp( ik-\frac{ic}{( 1+ |z_{n-1}|^2 )} )$$
The default selection for the a, b, c and k parameters is known to
produce a deterministic chaotic time series.
References
Strogatz, S.: Nonlinear dynamics and chaos: with applications
to physics, biology, chemistry and engineering (Studies in Nonlinearity)