dynr.trajectory function

A Function to perform numerical integration of the chosen ODE system, for a user-specified set of initial conditions. Plots the resulting solution(s) in the phase plane. This function from the phaseR package written by Michael J. Grayling.

dynr.trajectory(deriv, y0 = NULL, n = NULL, tlim, tstep = 0.01,
  parameters = NULL, system = "two.dim", col = "black", add = TRUE,
  state.names = c("x", "y"), ...)

Arguments

• deriv: A function computing the derivative at a point for the specified ODE system. See the phaseR package guide for more examples.
• y0: The initial condition(s) (ICs). In one-dimensional system, this can either be a single number indicating a single IC or a vector indicating multiple ICs. In 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 set of ICs. 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 tlim[1], 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.
• tlim: Sets the limits of the independent variable for which the solution should be plotted. Should be a vector of length two. If tlim[2] > tlim[1], then tstep should be negative to indicate a backwards trajectory.
• tstep: The step length of the independent variable, used in numerical integration. 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".
• col: The color(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. Defaults to TRUE. TRUE = the trajectories added to an existing plot; FALSE = a new plot is created.
• state.names: State names for the ODE functions that do not use positional states
• ...: Additional arguments to be passed to either plot or arrows.

Returns

Returns a list with the following components: add, col, deriv, n, parameters, system, tlim, tstep, t, x, y, ylab, y0. Most of these components correspond simply to their original input values.

The only new elements are: t = A vector containing the values of the independent variable at each integration step.

x = In the two dimensional system case, a matrix whose columns are the numerically computed values of the first dependent variable for each set of ICs.

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.

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

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