run_meanfield {chouca}

Mean field model

Description

Run the mean field model corresponding to a cellular automaton

Usage

run_meanfield(mod, init, times, ...)

Arguments

mod

The cellular automaton model (produced by camodel

init

The initial landscape, or a vector of covers summing to one, whose length is equal to the number of states in the model.

times

The points in time for which output is wanted

...

other arguments are passed to ode

Details

The mean field approximation to a cellular automaton simply describes the dynamics of the global covers using differential equations, assumming that both global and local covers are equal (in chouca model specifications, this assumes p = q).

For example, if we consider a model with two states 'a' and 'b' and transitions from and to each other, then the following system of equation is used to describe the variations of the proportions of cells in each state:

\frac{da}{dt} = p_b P(b \to a) - p_a P(a \to b)

\frac{db}{dt} = p_a P(a \to b) - p_b P(b \to a)

Running mean-field approximations is useful to understand general dynamics in the absence of neighborhood interactions between cells, or simply to obtain an fast but approximate simulation of the model.

Note that this function uses directly the expressions of the probabilities, so any cellular automaton is supported, regardless of whether or not it can be simulated exactly by run_camodel.

Value

This function returns the results of the ode function, which is a matrix with class 'deSolve'

Examples

if ( requireNamespace("deSolve") ) { 
  # Get the mean-field approximation to the arid vegetation model 
  arid <- ca_library("aridvege") 
  mod <- ca_library("aridvege")
  init <- generate_initmat(mod, rep(1, 3)/3, nrow = 100, ncol = 100)
  times <- seq(0, 128)
  out <- run_meanfield(mod, init, times)
  # This uses the default plot method in deSolve
  plot(out)
  
  # A different model and way to specifiy initial conditions.
  coralmod <- ca_library("coralreef")
  init <- c(ALGAE = 0.2, CORAL = 0.5, BARE = 0.3)
  times <- 10^seq(0, 4, length.out = 64)
  out <- run_meanfield(coralmod, init, times, method = "lsoda")
  plot(out, ylim = c(0, 1))
}