henonMap#

peccary.examples.henonMap(n, a=1.4, b=0.3)[source]#

Generate timeseries from Hénon map.

Default parameters are for the classical Hénon map, where values are chaotic.

Parameters:

nint: Number of timesteps to generate
afloat, optional: Parameter for Hénon map, by default 1.4
bfloat, optional: Parameter for Hénon map, by default 0.3

Returns:

peccary.timeseries.Timeseries: Timeseries for Hénon map, stored in x attribute of Timeseries class

References

[1] For more information on the Hénon map, see Wolfram Mathworld’s entry.

Examples

To create a chaotic timeseries of 10 points using the Hénon map, e.g.,

>>> import peccary.examples as ex
>>> henon = ex.henonMap(10)

The data can be called as follows:

>>> henon.x
array([ 1.        ,  0.6       ,  0.796     ,  0.2929376 ,  1.11866259,
   -0.6640871 ,  0.71818243,  0.07867346,  1.20678941, -1.01527491])

The default parameters are \(a=1.4\) and :math:b=0.3`, which give a chaotic timeseries (i.e., the classical Hénon map). Other values for the parameters can result in chaotic, intermittent chaotic and periodic, or converging periodic behavior.