Generates a time series using the Ikeda map
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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. |
a |
The a parameter. Default: 0.85. |
b |
The b parameter. Default: 0.9. |
c |
The c parameter. Default: 7.7. |
k |
The k parameter. Default: 0.4. |
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 ikeda system is shown. |
The Ikeda map is defined as follows:
z[n+1] = a + b*z[n]*exp(ik-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.
a list with 2 vectors named x and y the x-components and the y-components of the Ikeda map, respectively.
Some initial values may lead to an unstable system that will tend to infinity.
Constantino A. Garcia
Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)
henon, logisticMap, lorenz,
rossler, cliffordMap, sinaiMap,
gaussMap
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