phaseR (version 2.1.3)

example5: Example ODE system 5

Description

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

Usage

example5(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

example5 evaluates the derivatives of the following coupled ODE system at the point (t, x, y):

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

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

See Also

ode

Examples

# Plot the velocity field, nullclines, manifolds and several trajectories
example5_flowField         <- flowField(example5,
                                        xlim   = c(-3, 3),
                                        ylim   = c(-3, 3),
                                        points = 19,
                                        add    = FALSE)
y0                         <- matrix(c(1, 0, -1, 0, 2, 2,
                                       -2, 2, 0, 3, 0, -3), 6, 2,
                                     byrow = TRUE)
example5_nullclines        <- nullclines(example5,
                                         xlim = c(-3, 3),
                                         ylim = c(-3, 3))
example5_trajectory        <- trajectory(example5,
                                         y0   = y0,
                                         tlim = c(0,10))
# Plot x and y against t
example5_numericalSolution <- numericalSolution(example5,
                                                y0   = c(0, 3),
                                                tlim = c(0, 3))
# Determine the stability of the equilibrium point
example5_stability         <- stability(example5,
                                        ystar = c(0, 0))