Description Usage Arguments Value Author(s) See Also Examples

Performs numerical integration of the chosen ODE system, for a user specifiable range of initial conditions. Plots the resulting solution in the phase plane.

1 2 3 |

`deriv` |
A function computing the derivative at a point for the ODE system to be analysed. Discussion of the required structure of these functions can be found in the package guide. |

`y0` |
The initial condition(s). In the case of a one dimensional system, this can either be a single number indicating the location of the dependent variable initially, or a vector indicating multiple initial locations of the independent variable. In the case of a two dimensional system, this can either be a vector of length two reflecting the location of the two dependent variables initially. Or it can be matrix where each row reflects a different initial condition. Alternatively this can be left blank and the user can use locator to specify initial condition(s) on a plot. In this case, for one dimensional systems, all initial conditions are taken at t.start, even if not selected so on the graph. Defaults to NULL. |

`n` |
If y0 is left NULL so initial conditions can be specified using locator, n sets the number of initial conditions to be chosen. Defaults to NULL. |

`t.start` |
The value of the independent variable to begin the numerical integration at. Defaults to 0. |

`t.end` |
The value of the independent variable to end numerical integration at. |

`t.step` |
The step length of the independent variable, used in numerical integration. Decreasing t.step theoretically makes the numerical integration more accurate, but increases computation time. Defaults to 0.01. |

`parameters` |
Parameters of the ODE system, to be passed to deriv. Supplied as a vector; the order of the parameters can be found from the deriv file. Defaults to NULL. |

`system` |
Set to either "one.dim" or "two.dim" to indicate the type of system being analysed. Defaults to "two.dim". |

`colour` |
The colour(s) to plot the trajectories in. Will be reset accordingly if it is a vector not of the length of the number of initial conditions. Defaults to "black". |

`add` |
Logical. If TRUE, the trajectories added to an existing plot. If FALSE, a new plot is created. Defaults to TRUE. |

`...` |
Additional arguments to be passed to plot. |

Returns a list with the following components (the exact make up is dependent upon the type of system being analysed):

`add` |
As per input. |

`colour` |
As per input, but with possible editing if a colour vector of the wrong length was supplied. |

`deriv` |
As per input. |

`n` |
As per input. |

`parameters` |
As per input. |

`system` |
As per input. |

`t.end` |
As per input. |

`t.start` |
As per input. |

`t.step` |
As per input. |

`t` |
A vector containing the values of the independent variable at each integration step. |

`x` |
In the two dimensional system casem a matrix whose columns are the numerically computed values of the first dependent variable for each initial condition. |

`y0` |
As per input, but converted to a matrix if supplied as a vector initially. |

`y` |
In the two dimensional system case, a matrix whose columns are the numerically computed values of the second dependent variable for each initial condition. In the one dimensional system case, a matrix whose columns are the numerically computed values of the dependent variable for each initial condition. |

Michael J. Grayling

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# Plot the flow field, nullclines and several trajectories for the one
# dimensional autonomous ODE system logistic.
logistic.flowField <- flowField(logistic, x.lim = c(0, 5), y.lim = c(-1, 3),
parameters = c(1, 2), points = 21, system = "one.dim",
add = FALSE)
logistic.nullclines <- nullclines(logistic, x.lim = c(0, 5), y.lim = c(-1, 3),
parameters = c(1, 2), system = "one.dim")
logistic.trajectory <- trajectory(logistic, y0 = c(-0.5, 0.5, 1.5, 2.5), t.end = 5,
parameters = c(1, 2), system = "one.dim")
# Plot the velocity field, nullclines and several trajectories for the two dimensional
# autonomous ODE system simplePendulum.
simplePendulum.flowField <- flowField(simplePendulum, x.lim = c(-7, 7),
y.lim = c(-7, 7), parameters = 5, points = 19,
add = FALSE)
y0 <- matrix(c(0, 1, 0, 4, -6, 1, 5, 0.5, 0, -3), ncol = 2,
nrow = 5, byrow = TRUE)
simplePendulum.nullclines <- nullclines(simplePendulum, x.lim = c(-7, 7),
y.lim = c(-7, 7), parameters = 5, points = 500)
simplePendulum.trajectory <- trajectory(simplePendulum, y0 = y0, t.end = 10,
parameters = 5)
``` |

phaseR documentation built on May 29, 2017, 6:59 p.m.

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