phaseR (version 2.2.1)

example9: Example ODE system 9

Description

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

Usage

example9(t, y, parameters)

Value

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

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.

Author

Michael J Grayling

Details

example9 evaluates the derivatives of the following coupled ODE system at the point (t, x, y):

dx/dt = -2x + 3y, dy/dt = 7x + 6y.

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

See Also

ode

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))