The R Book

Differential equations

We need to solve a system of ordinary differential equations (ODEs) and choose to use the classical Runge–Kutta fourth-order integration function rk4 from the odesolve package:

install.packages("odesolve")
library(odesolve)

The example involves a simple resource-limited plant herbivore where V = vegetation and N = herbivore population. We need to specify two differential equations: one for the vegetation (dV/dt) and one for the herbivore population (dN/dt):

The steps involved in solving these ODEs in R are as follows:

• Define a function (called phmodel in this case).
• Name the response variables V and N from x[1] and x[2].
• Write the vegetation equation as dv using with.
• Write the herbivore equation as dn using with.
• Combine these vectors into a list called res.
• Generate a time series over which to solve the equations.
• Here, t is from 0 to 500 in steps of 1.
• Set the parameter values in parms.
• Set the starting values for V and N in y and xstart.
• Use rk4 to create a dataframe with the V and N time series.

phmodel <-function(t, x, parms) {
v<-x[1]
n<-x[2]
with(as.list(parms), {
dv<-r*v*(K-v)/K - b*v*n
dn<-c*v*n – d*n
res<-c(dv, dn)

list(res)
})}

times <-seq(0, ...