data.gen.Duffing {synthesis}

Duffing map

Description

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

Usage

data.gen.Duffing(
  nobs = 5000,
  a = 2.75,
  b = 0.2,
  start = runif(n = 2, min = -0.5, max = 0.5),
  s,
  do.plot = TRUE
)

Arguments

nobs

Length of the generated time series. Default: 5000 samples.

a

The a parameter. Default: 2.75.

b

The b parameter. Default: 0.2.

start

A 2-dimensional vector indicating the starting values for the x and y Duffing coordinates. Default: If the starting point is not specified, it is generated randomly.

s

The level of noise, default 0.

do.plot

Logical value. If TRUE (default value), a plot of the generated Duffing system is shown.

Details

The Duffing map is defined as follows:

x_n = y_{n - 1}

y_n = -b \cdot x_{n - 1} + a \cdot y_{n - 1} - y_{n - 1}^3

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 Duffing map, respectively.

Note

Some initial values may lead to an unstable system that will tend to infinity.

References

Constantino A. Garcia (2019). nonlinearTseries: Nonlinear Time Series Analysis. R package version 0.2.7. https://CRAN.R-project.org/package=nonlinearTseries

Examples

Duffing.map=data.gen.Duffing(nobs = 1000, do.plot=TRUE)