data.gen.Rossler {WASP}

Generate predictor and response data: Rossler system

Description

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

Usage

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).

Details

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

\dot{x} = -(y + z)

\dot{y} = x+a \cdot y

\dot{z} = b + z*(x-w)

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.

Value

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.

Note

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

References

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

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"))