R/Ross76-data.R

In GPoM: Generalized Polynomial Modelling

#' Time series of the Rossler-1976 system
#'
#' @name Rossler-1976 data set
#' @docType data
#'
#' @encoding UTF-8
#' @description
#' The Rössler system is the 3-dimensional chaotic system \cr
#' \eqn{dx/dt = - y - z} \cr
#' \eqn{dy/dt = x + a y} \cr
#' \eqn{dz/dt = b + z (x - c)}, \cr
#' discovered by Otto E. Rössler in 1976 [1].
#' The following parameters and initial conditions
#' were used to produce the present data set:\cr
#' a = 0.520, b = 2, c = 4 \cr
#' and (x0, y0, z0) = (-0.04298734, 1.025536, 0.09057987).\cr
#' The following four columns are provided:\cr
#' (1) time t, (2) x(t), (3) y(t) and (4) z(t).\cr
#' For this parameterization, the Rössler system produces
#' a chaotic behavior characterized by a regime
#' non-coherent in phase (oscillations duration can be
#' very different from one oscillation to another).
#'
#' @author Sylvain Mangiarotti, Flavie Le Jean,
#' Malika Chassan, Laurent Drapeau, Mireille Huc.
#'
#' @references
#' [1] O. Rössler, 1976. An Equation for Continuous Chaos,
#' Physics Letters, 71A, 2-3, 155-157. \cr
#'
#' @keywords data
"Ross76"