This function simulates time series from the R<U+00F6>ssler 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.
rossler.ts(a.min = 0.1, a.max = 0.2, b.min = 0.1, b.max = 0.2,
c.min = 4, c.max = 5.7, xo.min = -2, xo.max = 2, yo.min = -10,
yo.max = 10, zo.min = -0.2, zo.max = 0.2, time = seq(0, 100,
0.01), transient = 1000, B = 100, doplot = TRUE)
a non-negative integer denoting a lower bound for the parameter a
(Default 0).
a non-negative integer denoting an upper bound for the parameter a
(Default 0.2).
a non-negative integer denoting a lower bound for the parameter b
(Default 0).
a non-negative integer denoting an upper bound for the parameter b
(Default 0.2).
a non-negative integer denoting a lower bound for the parameter c
(Default 4).
a non-negative integer denoting an upper bound for the parameter c
(Default 5.7).
a non-negative integer denoting a lower bound for the initial condition xo
(Default -2).
a non-negative integer denoting an upper bound for the initial condition xo
(Default 2).
a non-negative integer denoting a lower bound for the initial condition yo
(Default -10).
a non-negative integer denoting an upper bound for the initial condition yo
(Default 10).
a non-negative integer denoting a lower bound for the initial condition zo
(Default -0.2).
a non-negative integer denoting an upper bound for the initial condition zo
(Default 0.2).
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).
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).
a non-negative integer denoting the number of series that will be generated for different values of parameters a
, b
and c
. The number of simulated series must be at least 100 (Default 100).
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
).
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 a
, the value of the parameter b
, the value of the parameter c
, 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 R<U+00F6>ssler system with three columns corresponding to 'x-coordinate', 'y-coordinate' and 'z-coordinate'.
R<U+00F6>ssler, O. 1976 An equation for continuous chaos. Physics Letters A 57(5):397-398.
# NOT RUN {
## Simulates 100 time series from the R<U+00F6>ssler system for different
## values of the parameters a, b and c in which this system exhibits
## a chaotic behaviour:
ts<-rossler.ts(a.min=0.2,a.max=0.2,b.min=0.2,b.max=0.2,c.min=5.7,c.max=5.7,
time=seq(0,10,0.01),transient=100,B=100,doplot=TRUE)
# }
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