## Simulation of a Bivariate Ornstein-Uhlenbeck Process

### Description

This function simulates a bivariate Ornstein-Uhlenbeck process for animal movement.

### Usage

```simm.mou(date = 1:100, b = c(0, 0),
a = diag(0.5, 2), x0 = b,
sigma = diag(2), id = "A1",
burst = id, proj4string=CRS())
```

### Arguments

 `date` a vector indicating the date (in seconds) at which relocations should be simulated. This vector can be of class `POSIXct` `b` a vector of length 2 containing the coordinates of the attraction point `a` a 2*2 matrix `x0` a vector of length 2 containing the coordinates of the startpoint of the trajectory `sigma` a 2*2 positive definite matrix `id` a character string indicating the identity of the simulated animal (see `help(ltraj)`) `burst` a character string indicating the identity of the simulated burst (see `help(ltraj)`) `proj4string` a valid CRS object containing the projection information (see `?CRS` from the package `sp`).

### Details

The Ornstein-Uhlenbeck process can be used to take into account an "attraction point" into the animal movements (Dunn and Gipson 1977). This process can be simulated using the stochastic differential equation:

dz = a (b - z(t)) dt + Sigma dB2(t)

The vector `b` contains the coordinates of the attraction point. The matrix `a` (2 rows and 2 columns) contains coefficients controlling the force of the attraction. The matrix `Sigma` controls the noise added to the movement (see `?simm.mba` for details on this matrix).

### Value

An object of class `ltraj`

### Author(s)

Clement Calenge clement.calenge@ofb.gouv.fr
Stephane Dray dray@biomserv.univ-lyon1.fr
Manuela Royer royer@biomserv.univ-lyon1.fr
Daniel Chessel chessel@biomserv.univ-lyon1.fr

### References

Dunn, J.E., & Gipson, P.S. (1977) Analysis of radio telemetry data in studies of home range. Biometrics 33: 85–101.

`simm.brown`, `ltraj`, `simm.crw`, `simm.mba`

### Examples

```
suppressWarnings(RNGversion("3.5.0"))
set.seed(253)
u <- simm.mou(1:50, burst="Start at the attraction point")
v <- simm.mou(1:50, x0=c(-3,3),
burst="Start elsewhere")
w <- simm.mou(1:50, a=diag(c(0.5,0.1)), x0=c(-3,3),
burst="Variable attraction")
x <- simm.mou(1:50, a=diag(c(0.1,0.5)), x0=c(-3,7),
burst="Both")
z <- c(u,v,w,x)

plot(z, addpoints = FALSE, perani = FALSE)

```