example12 {phaseR}

Example ODE system 12

Description

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

Usage

example12(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 values of x and y, the dependent variables, to evaluate the derivative at. Should be a numeric vector of length two.

parameters

The values of the parameters of the system. Not used here.

Details

example12 evaluates the derivatives of the following coupled ODE system at the point (t, x, y):

dx/dt = x - y, dy/dt = x² + y² - 2.

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

Value

Returns a list containing the values of the two derivatives at (t, x, y).

Author(s)

Michael J Grayling

See Also

ode

Examples

# Plot the velocity field, nullclines and several trajectories
example12_flowField   <- flowField(example12,
                                   xlim   = c(-4, 4),
                                   ylim   = c(-4, 4),
                                   points = 17,
                                   add    = FALSE)
y0                    <- matrix(c(2, 2, -3, 0,
                                  0, 2, 0, -3), 4, 2,
                                byrow = TRUE)
example12_nullclines  <- nullclines(example12,
                                    xlim   = c(-4, 4),
                                    ylim   = c(-4, 4),
                                    points = 200)
example12_trajectory  <- trajectory(example12,
                                    y0   = y0,
                                    tlim = c(0, 10))
# Determine the stability of the equilibrium points
example12_stability_1 <- stability(example12,
                                   ystar = c(1, 1))
example12_stability_2 <- stability(example12,
                                   ystar = c(-1, -1))