pomp (version 2.4)

verhulst: Verhulst-Pearl model

Description

The Verhulst-Pearl (logistic) model of population growth.

Usage

verhulst(n_0 = 10000, K = 10000, r = 0.9, sigma = 0.4, tau = 0.1,
  dt = 0.01)

Arguments

n_0

initial condition

K

carrying capacity

r

intrinsic growth rate

sigma

environmental process noise s.d.

tau

measurement error s.d.

dt

Euler time-step

Value

A ‘pomp’ object containing the model and simulated data. The following basic components are included in the ‘pomp’ object: ‘rinit’, ‘rprocess’, ‘rmeasure’, ‘dmeasure’, and ‘skeleton’.

Details

A stochastic version of the Verhulst-Pearl logistic model. This evolves in continuous time, according to the stochastic differential equation $$dn = r\,n\,\left(1-\frac{n}{K}\right)\,dt+\sigma\,n\,dW.$$

Numerically, we simulate the stochastic dynamics using an Euler approximation.

The measurements are assumed to be log-normally distributed.

See Also

Other pomp examples: blowflies, dacca, ebola, gompertz, measles, ou2, ricker, rw2, sir_models

Examples

# NOT RUN {
verhulst() -> po
plot(po)
plot(simulate(po))
pfilter(po,Np=1000) -> pf
logLik(pf)
spy(po)
# }