verhulst function

Verhulst-Pearl model

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

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

Returns

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

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

The measurements are assumed to be log-normally distributed:

Examples

# takes too long for R CMD check
  verhulst() -> po
  plot(po)
  plot(simulate(po))
  pfilter(po,Np=1000) -> pf
  logLik(pf)
  spy(po)

See Also

More examples provided with pomp: blowflies, childhood_disease_data, compartmental_models, dacca(), ebola, gompertz(), ou2(), pomp_examples, ricker(), rw2()