logistic {phaseR}

The logistic growth model

Description

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

Usage

logistic(t, y, parameters)

Arguments

t

The value of t, the independent variable, to evaluate the derivative at. Should be a numeric vector of length one.

y

The value of y, the dependent variable, to evaluate the derivative at. Should be a numeric vector of length one.

parameters

The values of the parameters of the system. Should be a numeric 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

See Also

ode

Examples

# 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")