# 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

`ode`

## 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.