DChaos (version 0.1-1)

lorenz.ts: Simulation of time series from the Lorenz system

Description

This function simulates time series from the Lorenz system considering the argument set selected by the user. Some values for the parameters and initial conditions may lead to an unstable system that will tend to infinity.

Usage

lorenz.ts(sigma.min = 8, sigma.max = 10, rho.min = 25,
  rho.max = 27, beta.min = 1, beta.max = 2.67, xo.min = -14,
  xo.max = -10, yo.min = -13, yo.max = -10, zo.min = 3,
  zo.max = 10, time = seq(0, 100, 0.01), transient = 1000, B = 100,
  doplot = TRUE)

Arguments

sigma.min

a non-negative integer denoting a lower bound for the parameter sigma (Default 8).

sigma.max

a non-negative integer denoting an upper bound for the parameter sigma (Default 10).

rho.min

a non-negative integer denoting a lower bound for the parameter rho (Default 25).

rho.max

a non-negative integer denoting an upper bound for the parameter rho (Default 27).

beta.min

a non-negative integer denoting a lower bound for the parameter beta (Default 1).

beta.max

a non-negative integer denoting an upper bound for the parameter beta (Default 2.67).

xo.min

a non-negative integer denoting a lower bound for the initial condition xo (Default -14).

xo.max

a non-negative integer denoting an upper bound for the initial condition xo (Default -10).

yo.min

a non-negative integer denoting a lower bound for the initial condition yo (Default -13).

yo.max

a non-negative integer denoting an upper bound for the initial condition yo (Default -10).

zo.min

a non-negative integer denoting a lower bound for the initial condition zo (Default 3).

zo.max

a non-negative integer denoting an upper bound for the initial condition zo (Default 10).

time

a numeric vector denoting the time-lapse and the time-step (Default 'time-lapse' equal to 10001 with a 'time-step' of 0.01 seconds).

transient

a non-negative integer denoting the number of observations that will be discarded to ensure that the values of each time serie are in the attractor (Default 1000).

B

a non-negative integer denoting the number of series that will be generated for different values of parameters sigma, rho and beta. The number of simulated series must be at least 100 (Default 100).

doplot

a logical value denoting if you want to draw a plot TRUE or not FALSE. If it is TRUE shows six graphs: the evolution of the temporal trajectories for the whole period, the attractor and its projections on the Cartesian plane. All of them consider the 'x-coordinate', the 'y-coordinate' and the 'z-coordinate' (Default TRUE).

Value

A list containing as many items as series we want to simulate B. Each of them has the following attributes: the value of the parameter sigma, the value of the parameter rho, the value of the parameter beta, the value of the initial condition xo, the value of the initial condition yo, the value of the initial condition zo and a time serie from the iterated Lorenz system with three columns corresponding to 'x-coordinate', 'y-coordinate' and 'z-coordinate'.

References

Lorenz, E. 1963 Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20(2):130-141.

See Also

logistic.ts, henon.ts, rossler.ts

Examples

# NOT RUN {
## Simulates 100 time series from the Lorenz system for different
## values of the parameters sigma, rho and beta in which this system
## exhibits a chaotic behaviour:
ts<-lorenz.ts(sigma.min=10,sigma.max=10,rho.min=27,rho.max=27,beta.min=2.67,
              beta.max=2.67,time=seq(0,10,0.01),transient=100,B=100, doplot=TRUE)
# }