dynr.flowField {dynr}

A Function to plot the flow or velocity field for a one or two dimensional autonomous ODE system from the phaseR package written by Michael J. Grayling.

Description

A Function to plot the flow or velocity field for a one or two dimensional autonomous ODE system from the phaseR package written by Michael J. Grayling.

Usage

dynr.flowField(deriv, xlim, ylim, parameters = NULL, system = "two.dim",
  points = 21, col = "gray", arrow.type = "equal", arrow.head = 0.05,
  frac = 1, add = TRUE, xlab = "x", ylab = "y", state.names = c("x",
  "y"), ...)

Arguments

deriv

A function computing the derivative at a point for the ODE system to be analysed. For examples see the phaseR package guide.

xlim

A vector of length two setting the lower and upper limits of the variable to be plotted on the horizontal axis (usually the first variable returned by the function deriv)

ylim

A vector of length two setting the lower and upper limits of the variable to be plotted on the vertical axis (usually the second variable returned by the function deriv)

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".

points

Sets the density of the line segments to be plotted. Defaults to 11.

col

Sets the color of the plotted line segments. Defaults to "gray". Should be a vector of length one. Will be reset accordingly if it is a vector of the wrong length.

arrow.type

Sets the type of line segments plotted. Options include: "proportional" = the length of the line segments reflects the magnitude of the derivative. "equal" the line segments take equal lengths, simply reflecting the gradient of the derivative(s). Defaults to "equal".

arrow.head

Sets the length of the arrow heads. Passed to arrows. Defaults to 0.05.

frac

Sets the fraction of the theoretical maximum length line segments can take without overlapping, that they can actually attain. In practice, frac can be set to greater than 1 without line segments overlapping.

add

Logical. Defaults to TRUE. TRUE = the flow field is added to an existing plot; FALSE = a new plot is created.

xlab

Label for the x-axis of the resulting plot. Defaults to "x".

ylab

Label for the y-axis of the resulting plot. Defaults to "y".

state.names

State names for ode functions that do not use positional states

...

Additional arguments to be passed to either plot or arrows.

Value

Returns a list with the following components: add, arrow.head, arrow.type, col, deriv, dx, dy, frac, parameters, points, system, x, xlab, xlim, y, ylab, ylim. Most of these components correspond simply to their original input values.

The only new elements are:

dx = A matrix. In the case of a two dimensional system, the values of the derivative of the first dependent derivative at all evaluated points.

dy = A matrix. In the case of a two dimensional system, the values of the derivative of the second dependent variable at all evaluated points. In the case of a one dimensional system, the values of the derivative of the dependent variable at all evaluated points.

x = A vector. In the case of a two dimensional system, the values of the first dependent variable at which the derivatives were computed. In the case of a one dimensional system, the values of the independent variable at which the derivatives were computed.

y = A vector. In the case of a two dimensional system, the values of the second dependent variable at which the derivatives were computed. In the case of a one dimensional system, the values of the dependent variable at which the derivatives were computed.

Note

The phaseR package was taken off cran as off 10/1/2019 so we are exporting some selected functions from phaseR_2.0 published on 8/20/2018. For details of these functions please see original documentations on the phaseR package.

References

Grayling, Michael J. (2014). phaseR: An R Package for Phase Plane Analysis of Autonomous ODE Systems. The R Journal, 6(2), 43-51. DOI: 10.32614/RJ-2014-023. Available at https://doi.org/10.32614/RJ-2014-023