example2 {phaseR}

Example ODE system 2

Description

The derivative function of an example one-dimensional autonomous ODE system.

Usage

example2(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. Not used here.

Details

example2 evaluates the derivative of the following ODE at the point (t, y):

dy/dt = y(1 - y)(2 - y).

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 flow field and several trajectories
example2_flowField     <- flowField(example2,
                                    xlim   = c(0, 4),
                                    ylim   = c(-1, 3),
                                    system = "one.dim",
                                    add    = FALSE,
                                    xlab   = "t")
example2_trajectory    <- trajectory(example2,
                                     y0     = c(-0.5, 0.5, 1.5, 2.5),
                                     tlim   = c(0, 4),
                                     system = "one.dim")
# Plot the phase portrait
example2_phasePortrait <- phasePortrait(example2,
                                        ylim = c(-0.5, 2.5),
                                        frac = 0.5)
# Determine the stability of the equilibrium points
example2_stability_1   <- stability(example2,
                                    ystar  = 0,
                                    system = "one.dim")
example2_stability_2   <- stability(example2,
                                    ystar  = 1,
                                    system = "one.dim")
example2_stability_3   <- stability(example2,
                                    ystar  = 2,
                                    system = "one.dim")