simplePdmp: A simple PDMP

In CharlotteJana/pdmpsim: Simulate Piecewise Deterministic Markov Processes

A simple PDMP

Description

This is a simple example for a piecewise deterministic markov process defined as pdmpModel. It is included to the package for demonstration purposes and is used in some unit tests and function examples.

Usage

simplePdmp

Format

An object of class pdmpModel.

Slots

parms

There are no parameters for this model.

init

There is one continous variable f with initial value 0 and one discrete variable d initial value 0.

discStates

The discrete variable d has codomain {-1, 0, 1}.

dynfunc

The continous variable f evolves as linear function f(t) = t if d = 1, as f(t) = -t if d = -1 and is constant zero if d = 0. Its dynamic can therefore be described as \frac{df}{dt} = d.

jumpfunc

There are two jumptypes. The first jumps from d to d - 1, the second from d to d + 1. Both reset f to zero.

ratefunc

A vector of length two determining the probability of a jump being of type 1 or 2. If d = -1, it has value (0, 2) forcing the jumptype to be of type 2. The same takes place for d = 1: ratefunc returnes (2, 0) and the jumptype is therefore always of type 1. In case d = 0, ratefunc returnes (1, 1) which leads to a probability of \frac{1}{2} to have a jumptype of type 1 or 2.

times

The simulations will start at time t = 0 and end at t = 10 with step length 0.01.

See Also

toggleSwitch for a more sophisticated example of a pdmpModel and pdmpModel for the formal description of the S4 class.

Examples

## the code used to generate this model:

simplePdmp <- pdmpModel(
    descr = "A simple PDMP",
    init = c(f = 0, d = 0),
    discStates = list(d = c(-1, 0, 1)),
    times = c(from = 0, to = 10, by = 0.01),
    dynfunc = function(t, x, parms) c(x["d"], 0),
    ratefunc = function(t, x, parms) c(1+x["d"], 1-x["d"]),
    jumpfunc = function(t, x, parms, jtype){
         c(0, switch(jtype, x["d"]-1, x["d"]+1))
    })

## load it and plot a simulation:
data("simplePdmp")
plot(sim(simplePdmp))

CharlotteJana/pdmpsim documentation built on Oct. 21, 2024, 4:54 p.m.