verhulst {pomp} | R Documentation |
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 timestep |
Details
A stochastic version of the Verhulst-Pearl logistic model. This evolves in continuous time, according to the stochastic differential equation
dn_t = r\,n_t\,\left(1-\frac{n_t}{K}\right)\,dt+\sigma\,n_t\,dW_t.
Numerically, we simulate the stochastic dynamics using an Euler approximation.
The measurements are assumed to be log-normally distributed:
N_t \sim \mathrm{Lognormal}\left(\log{n_t},\tau\right).
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’.
See Also
More examples provided with pomp:
blowflies
,
childhood_disease_data
,
compartmental_models
,
dacca()
,
ebola
,
gompertz()
,
ou2()
,
pomp_examples
,
ricker()
,
rw2()
Examples
# takes too long for R CMD check
verhulst() -> po
plot(po)
plot(simulate(po))
pfilter(po,Np=1000) -> pf
logLik(pf)
spy(po)