arguments.map {BTSR} | R Documentation |
Available map functions in BTSR package
Description
This documentation describes the map
argument in BARC
models and the map functions implemented in the BTSR package.
Arguments
map |
a non-negative integer from 1 to 5 corresponding to the map
function. Default is |
The map function
The map function T:[0,1] \to [0,1]
in BARC models is a dynamical
system, i.e., a function, potentially depending on a r
-dimensional
vector of parameters \theta
. As for today, for all implemented maps,
r = 1
.
Available choices are
-
map = 1
,\theta = k
, fork
integer greater or equal to 2.T(u) = (ku)(\text{mod } 1)
-
map = 2
,0 \le \theta \le 1
T(u) = \dfrac{u}{\theta}I( u < \theta) + \theta\dfrac{(u - \theta)}{(1 - \theta)}I(u \ge \theta)
-
map = 3
(logistic map),0 \le \theta \le 4
,T(u) = \theta(1-\theta)
-
map = 4
(Manneville-Pomeau map),0 < \theta < 1
T(u) = (u + u^{1+\theta})(\text{mod } 1)
-
map = 5
(Lasota-Mackey's map),T(u) = \dfrac{u}{(1 - u)}I(u \le 0.5) + (2u - 1)I(u > 0.5)