data.gen.Rossler function

Generate predictor and response data: Rossler system

Generates a 3-dimensional time series using the Rossler equations.

data.gen.Rossler(
  a = 0.2,
  b = 0.2,
  w = 5.7,
  start = c(-2, -10, 0.2),
  time = seq(0, 50, length.out = 5000)
)

Arguments

• a: The a parameter. Default:0.2.
• b: The b parameter. Default: 0.2.
• w: The w parameter. Default: 5.7.
• start: A 3-dimensional numeric vector indicating the starting point for the time series. Default: c(-2, -10, 0.2).
• time: The temporal interval at which the system will be generated. Default: time=seq(0,50,length.out = 5000).

Returns

A list with four vectors named time, x, y

and z containing the time, the x-components, the y-components and the z-components of the Rossler system, respectively.

Details

The Rossler system is a system of ordinary differential equations defined as:

The default selection for the system parameters (a = 0.2, b = 0.2, w = 5.7) is known to produce a deterministic chaotic time series.

Note

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

Examples

### synthetic example - Rossler
ts.r <- data.gen.Rossler(
  a = 0.2, b = 0.2, w = 5.7, start = c(-2, -10, 0.2),
  time = seq(0, 50, length.out = 1000)
)

# add noise
ts.r$x <- ts(ts.r$x + rnorm(length(ts.r$time), mean = 0, sd = 1))
ts.r$y <- ts(ts.r$y + rnorm(length(ts.r$time), mean = 0, sd = 1))
ts.r$z <- ts(ts.r$z + rnorm(length(ts.r$time), mean = 0, sd = 1))

ts.plot(ts.r$x, ts.r$y, ts.r$z, col = c("black", "red", "blue"))

References

RÖSSLER, O. E. 1976. An equation for continuous chaos. Physics Letters A, 57, 397-398.