example11: Example ODE system 11 In phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

Description

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

Usage

 1 example11(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

example11 evaluates the derivatives of the following coupled ODE system at the point (t, x, y):

dx/dt = x(3 - x - 2y), dy/dt = -y(2 - x - y).

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

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 # Plot the velocity field, nullclines and several trajectories example11_flowField <- flowField(example11, xlim = c(-5, 5), ylim = c(-5, 5), points = 21, add = FALSE) y0 <- matrix(c(4, 4, -1, -1, -2, 1, 1, -1), 4, 2, byrow = TRUE) example11_nullclines <- nullclines(example11, xlim = c(-5, 5), ylim = c(-5, 5), points = 200) example11_trajectory <- trajectory(example11, y0 = y0, tlim = c(0, 10)) # Determine the stability of the equilibrium points example11_stability_1 <- stability(example11, ystar = c(0, 0)) example11_stability_2 <- stability(example11, ystar = c(0, 2)) example11_stability_3 <- stability(example11, ystar = c(1, 1)) example11_stability_4 <- stability(example11, ystar = c(3, 0))

Example output Note: col has been reset as required
T: 5   Delta: 6   Discriminant: 1   Classification: Unstable nodeT: -3   Delta: 2   Discriminant: 1   Classification: Stable nodeT: -2   Delta: -1   Discriminant: 8   Classification: SaddleT: -4   Delta: 3   Discriminant: 4   Classification: Stable node

phaseR documentation built on Oct. 12, 2019, 9:05 a.m.