StepCLE1D {smfsb}

Create a function for advancing the state of an SPN by using a simple Euler-Maruyama discretisation of the CLE on a 1D regular grid

Description

This function creates a function for advancing the state of an SPN model using a simple Euler-Maruyama discretisation of the CLE on a 1D regular grid. The resulting function (closure) can be used in conjunction with other functions (such as simTs1D) for simulating realisations of SPN models in space and time.

Usage

StepCLE1D(N,d,dt=0.01)

Arguments

N

An R list with named components representing a stochastic Petri net (SPN). Should contain N$Pre, a matrix representing the LHS stoichiometries, N$Post, a matrix representing the RHS stoichiometries, and N$h, a function representing the rates of the reaction processes. N$h should have first argument x, a vector representing the current state of the system, and second argument t, a scalar representing the current simulation time (in the typical time-homogeneous case, N$h will ignore this argument). N$h may possess additional arguments, representing reaction rates, for example. N does not need to contain an initial marking, N$M. N$M will be ignored by most functions which use the resulting function closure.

d

A vector of diffusion coefficients - one coefficient for each reacting species, in order. The coefficient is the reaction rate for a reaction for a molecule moving into an adjacent compartment. The hazard for a given molecule leaving the compartment is therefore twice this value (as it can leave to the left or the right).

dt

Time step for the Euler-Maruyama discretisation.

Value

An R function which can be used to advance the state of the SPN model N by using a simple Euler-Maruyama algorithm. The function closure has interface function(x0,t0,deltat,...), where x0 is a matrix with rows corresponding to species and columns corresponding to voxels, representing the initial condition, t0 represent the initial state and time, and deltat represents the amount of time by which the process should be advanced. The function closure returns a matrix representing the simulated state of the system at the new time.

See Also

StepGillespie1D,StepCLE, simTs1D, StepCLE2D

Examples

N=200
T=40
data(spnModels)
x0=matrix(0,nrow=2,ncol=N)
rownames(x0)=c("x1","x2")
x0[,round(N/2)]=LV$M
stepLV1D = StepCLE1D(LV,c(0.6,0.6),dt=0.05)
xx = simTs1D(x0,0,T,0.2,stepLV1D)
op=par(mfrow=c(1,2))
image(xx[1,,],main="Prey",xlab="Space",ylab="Time")
image(xx[2,,],main="Predator",xlab="Space",ylab="Time")
par(op)