vanDerPol: The Van Der Pol Oscillator

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/vanDerPol.R

Description

The derivative function of the Van Der Pol Oscillator, an example of a two-dimensional autonomous ODE system.

Usage

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vanDerPol(t, y, parameters)

Arguments

t

The value of t, the independent variable, to evaluate the derivative at. Should be a single number.

y

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

parameters

The values of the parameters of the system. Should be a single number prescribing the value of μ.

Details

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

dx/dt = y, dy/dt = μ(1 - x2)y - x.

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

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# Plot the velocity field, nullclines and several trajectories.
vanDerPol.flowField         <- flowField(vanDerPol,
                                         xlim = c(-5, 5),
                                         ylim = c(-5, 5),
                                         parameters = 3,
                                         points = 15,
                                         add = FALSE)
y0                          <- matrix(c(2, 0, 0, 2, 0.5, 0.5), 3, 2,
                                      byrow = TRUE)
vanDerPol.nullclines        <- nullclines(vanDerPol,
                                          xlim = c(-5, 5),
                                          ylim = c(-5, 5),
                                          parameters = 3,
                                          points = 500)
vanDerPol.trajectory        <- trajectory(vanDerPol,
                                          y0 = y0,
                                          tlim = c(0, 10),
                                          parameters = 3)
# Plot x and y against t
vanDerPol.numericalSolution <- numericalSolution(vanDerPol,
                                                 y0 = c(4, 2),
                                                 tlim = c(0, 100),
                                                 parameters = 3)
# Determine the stability of the equilibrium point
vanDerPol.stability         <- stability(vanDerPol,
                                         ystar = c(0, 0),
                                         parameters = 3)

phaseR documentation built on Aug. 20, 2018, 5:03 p.m.