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)
```

*pomp*version 5.11.0.0 Index]