playing with sublinear growth rate

sublinear.r

#sublinear
library(deSolve)
# adapted from 
# https://hankstevens.github.io/Primer-of-Ecology/DDgrowth.html

sublinear <- function(t, y, p){
  bi <- y[1]
  
  dN.dt <- with(as.list(p),
    r*b0^(1-k)*bi^k - z*bi
  )
  return(list(  dN.dt ))
  
}

p <- c(r = 1, k = 3/4, b0 = 1, z = 0.5)
y0 <- c(N=1)
tsteps = 0:50
out <- ode(y=y0, times=tsteps, func=sublinear, parms=p)
plot(N ~ time, data = out)

# equilibrium
with(as.list(p),
     (z/r*b0^(1-k))^(1/(k-1)))