simulate_Lorenz_noise {mvDFA}

Simulate the Lorenz System with noise

Description

Simulate the Lorenz System with noise

Usage

simulate_Lorenz_noise(
  N = 1000,
  delta_t = NULL,
  tmax = 50,
  X0 = 0,
  Y0 = 1,
  Z0 = 1,
  sdX = NULL,
  sdY = NULL,
  sdZ = NULL,
  sdnoiseX,
  sdnoiseY,
  sdnoiseZ,
  s = 10,
  r = 28,
  b = 8/3,
  naive = FALSE,
  return_time = TRUE
)

Arguments

N

Length of Times Series

delta_t

Step size for time scale. If NULL this is derived using N and tmax. DEFAULT to NULL.

tmax

Upper bound of the time scale. This argument is ignored if delta_t is provided. DEFAULT to 50.

X0

Initial value for X at t=0. DEFAULT to 0.

Y0

Initial value for Y at t=0. DEFAULT to 1.

Z0

Initial value for Z at t=0. DEFAULT to 1.

sdX

Use this argument to rescale the X-coordinate to have the desired standard deviation (exactly). This is ignored if set to NULL. DEFAULT to NULL.

sdY

Use this argument to rescale the Y-coordinate to have the desired standard deviation (exactly). This is ignored if set to NULL. DEFAULT to NULL.

sdZ

Use this argument to rescale the Z-coordinate to have the desired standard deviation (exactly). This is ignored if set to NULL. DEFAULT to NULL.

sdnoiseX

Standard deviation of Gaussian noise of X-coordinate. If set to 0, no noise is created.

sdnoiseY

Standard deviation of Gaussian noise of Y-coordinate. If set to 0, no noise is created.

sdnoiseZ

Standard deviation of Gaussian noise of Z-coordinate. If set to 0, no noise is created.

s

s-parameter of the Lorenz ODE. See Vignette for further details. DEFAULT to 10, which is the original value chosen by Lorenz.

r

r-parameter of the Lorenz ODE. See Vignette for further details. DEFAULT to 28, which is the original value chosen by Lorenz.

b

b-parameter of the Lorenz ODE. See Vignette for further details. DEFAULT to 8/3, which is the original value chosen by Lorenz.

naive

Logical whether naive calculation should be used. DEFAULT to FALSE.

return_time

Logical whether the time-coordinate should be included in the returned data.frame. DEFAULT to TRUE.

Value

Returns a three dimensional time series as data.frame following the Lorenz system (Lorenz, 1963, <doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2>).

References

Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of atmospheric sciences, 20(2), 130-141. <doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2>