IBBall: Increased bouncing ball

In CharlotteJana/pdmpsim: Simulate Piecewise Deterministic Markov Processes

Description

This is a minimal fictitious example, of a PDMP jumping at borders pdmpBorder. In difference to the examples simulated by pdmpModel the Prosess doesn't make stochastic jumps, what means thet we habe just one state, which changes the dynamic by reaching the border. This example makes it easy to see the functionality of borders. Here the minimum border 0 ist the ground where the velocity of the ball rises and therefore the height of each hop increases up to a second fixed border (20), where the process stops.

Usage

IBBall

Format

An object of class pdmpBorder.

Slots

init

There ist one continous variable, which describes the height of the ball and no discrete variable.

discStates

there are no discStates.

dynfunc

The dynamic of the continous variable depends on the velocity at the last jump (borderjump jump).

ratefunc

The ratefunc is 0, because the probability to jump ist 0, because the example models just one discret state.

parms

There is the parameter b, which is the factor of changing the velocity of our process each time the process hits the border zero and a and there are no change rates of the process.

times

The simulations will start at time t = 0 and end at the time, where the termination terminating value is reached.

borroot

It has dimension one and replaces the ground (=minimum), where the velocity is changed by b*velocity.

terroot

Every value, which forces the process to terminate is stored in the vector terroot. In this example it has dimension one and is the fixed value of 20 which forces the precess to terminate.

borderfunc

the borderfunc changes the values of the differential equation by reaching the borroot.

See Also

OÖK for another example of a pdmpBorder, where stochastic and border jumps appear. In pdmpBorder you can find a formal description of the S4 class.

Examples

IBBall <-pdmpBorder(
  descr = "increasing bouncing ball, just borderjumps",
  parms = list(a = -5, b = -1.1),
  init = c(height = 0, velocity = 10),
  discStates = list(),
  borroot = function(t, x, parms){return(c(x[1]))},
  terroot = function(t, x, parms){return(c(x[1] - 20))},
  times = seq(from = 0, to = 25, by = 0.01),
  dynfunc =  function(t, x, parms) {
    dheight <- with(as.list(c(x, parms)), c(velocity, a))
  return(c(dheight))
  },
  ratefunc = function(t, x, parms) {
    0
  },
  jumpfunc = function(t, x, parms) {return(with(as.list(c(x, parms)), c(dheight)))},
  borderfunc = function(t, x, parms){return(with(as.list(c(x, parms)), c(height = 0, velocity = b* velocity)))
})

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

CharlotteJana/pdmpsim documentation built on July 2, 2019, 5:37 a.m.