DChaos (version 0.1-1)

henon.ts: Simulation of time series from the H<U+00E9>non map

Description

This function simulates time series from the H<U+00E9>non map considering the argument set selected by the user. The initial conditions of each time serie are two random numbers between -0.5 and 0.5. Some values for the parameters and initial conditions may lead to an unstable system that will tend to infinity.

Usage

henon.ts(a.min = 0.4, a.max = 1.4, b.min = 0.1, b.max = 0.3,
  sample = 1000, transient = 100, B = 100, doplot = TRUE)

Arguments

a.min

a non-negative integer denoting a lower bound for the parameter a (Default 0.4).

a.max

a non-negative integer denoting an upper bound for the parameter a (Default 1.4).

b.min

a non-negative integer denoting a lower bound for the parameter b (Default 0.1).

b.max

a non-negative integer denoting an upper bound for the parameter b (Default 0.3).

sample

a non-negative integer denoting the length of each time serie (Default 1000).

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 100).

B

a non-negative integer denoting the number of series that will be generated for different values of the parameters a and b. 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 and the bifurcation diagram. All of them consider both the 'x-coordinate' and the 'y-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 a, the value of the parameter b, the value of the initial condition xo, the value of the initial condition yo and a time serie from the iterated H<U+00E9>non map with two columns corresponding to 'x-coordinate' and 'y-coordinate'.

References

H<U+00E9>non, M. 1976 A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics 50(1):69-77.

See Also

logistic.ts, rossler.ts, lorenz.ts

Examples

# NOT RUN {
## Simulates 100 time series from the H<U+00E9>non map for different
## values of the parameters a and b in which this system exhibits
## a chaotic behaviour:
ts<-henon.ts(a.min=0.7,a.max=1.4,b.min=0.1,b.max=0.3,B=100,doplot=TRUE)
# }