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.
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"), ...)
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.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.
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.
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