example9 function

Example ODE system 9

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

example9(t, y, parameters)

Arguments

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

• y: The values of and , 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.

Returns

Returns a list containing the values of the two derivatives at .

Details

example9 evaluates the derivatives of the following coupled ODE system at the point :

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

Examples

# Plot the velocity field, nullclines and several trajectories
example9_flowField  <- flowField(example9,
                                 xlim   = c(-3, 3),
                                 ylim   = c(-3, 3),
                                 points = 19,
                                 add    = FALSE)
y0                  <- matrix(c(1, 0, -3, 2,
                                2, -2, -2, -2), 4, 2,
                              byrow = TRUE)
example9_nullclines <- nullclines(example9,
                                  xlim = c(-3, 3),
                                  ylim = c(-3, 3))
example9_trajectory <- trajectory(example9,
                                  y0   = y0,
                                  tlim = c(0, 10))
# Determine the stability of the equilibrium point
example9_stability  <- stability(example9,
                                 ystar = c(0, 0))

See Also

ode

Author(s)

Michael J Grayling