# logistic: The Logistic Growth Model In phaseR: Phase Plane Analysis of One and Two Dimensional Autonomous ODE Systems

## Description

The derivative function of the logistic growth model, an example of a two-dimensional autonomous ODE system.

## Usage

 `1` ```logistic(t, y, parameters) ```

## Arguments

 `t` The value of t, the independent variable, to evaluate the derivative at. Should be a single number. `y` The value of y, the dependent variable, to evaluate the derivative at. Should be a single number. `parameters` The values of the parameters of the system. Should be a vector with parameters specified in the following order: β, K.

## Details

`logistic` evaluates the derivative of the following ODE at the point (t, y):

dy/dt = βy(1 - y/K).

Its format is designed to be compatible with `ode` from the `deSolve` package.

## Value

Returns a list containing the value of the derivative at (t, y).

## Author(s)

Michael J. Grayling

`ode`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33``` ```# Plot the velocity field, nullclines and several trajectories logistic.flowField <- flowField(logistic, xlim = c(0, 5), ylim = c(-1, 3), parameters = c(1, 2), points = 21, system = "one.dim", add = FALSE) logistic.nullclines <- nullclines(logistic, xlim = c(0, 5), ylim = c(-1, 3), parameters = c(1, 2), system = "one.dim") logistic.trajectory <- trajectory(logistic, y0 = c(-0.5, 0.5, 1.5, 2.5), tlim = c(0, 5), parameters = c(1, 2), system = "one.dim") # Plot the phase portrait logistic.phasePortrait <- phasePortrait(logistic, ylim = c(-0.5, 2.5), parameters = c(1, 2), points = 10, frac = 0.5) # Determine the stability of the equilibrium points logistic.stability.1 <- stability(logistic, ystar = 0, parameters = c(1, 2), system = "one.dim") logistic.stability.2 <- stability(logistic, ystar = 2, parameters = c(1, 2), system = "one.dim") ```