flowField: Flow field

In phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

Flow field

Description

Plots the flow or velocity field for a one- or two-dimensional autonomous ODE system.

Usage

flowField(
  deriv,
  xlim,
  ylim,
  parameters = NULL,
  system = "two.dim",
  points = 21,
  col = "gray",
  arrow.type = "equal",
  arrow.head = 0.05,
  frac = 1,
  add = TRUE,
  state.names = if (system == "two.dim") c("x", "y") else "y",
  xlab = if (system == "two.dim") state.names[1] else "t",
  ylab = if (system == "two.dim") state.names[2] else state.names[1],
  ...
)

Arguments

deriv	A function computing the derivative at a point for the ODE system to be analysed. Discussion of the required format of these functions can be found in the package vignette, or in the help file for the function ode.
xlim	In the case of a two-dimensional system, this sets the limits of the first dependent variable in which gradient reflecting line segments should be plotted. In the case of a one-dimensional system, this sets the limits of the independent variable in which these line segments should be plotted. Should be a numeric vector of length two.
ylim	In the case of a two-dimensional system this sets the limits of the second dependent variable in which gradient reflecting line segments should be plotted. In the case of a one-dimensional system, this sets the limits of the dependent variable in which these line segments should be plotted. Should be a numeric vector of length two.
parameters	Parameters of the ODE system, to be passed to deriv. Supplied as a numeric 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; points segments will be plotted in the x and y directions. Fine tuning here, by shifting points up and down, allows for the creation of more aesthetically pleasing plots. Defaults to 11.
col	Sets the colour of the plotted line segments. Should be a character vector of length one. Will be reset accordingly if it is of the wrong length. Defaults to "gray".
arrow.type	Sets the type of line segments plotted. If set to "proportional" the length of the line segments reflects the magnitude of the derivative. If set to "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. Fine tuning here assists the creation of aesthetically pleasing plots. Defaults to 1.
add	Logical. If TRUE, the flow field is added to an existing plot. If FALSE, a new plot is created. Defaults to TRUE.
state.names	The state names for ode functions that do not use positional states.
xlab	Label for the x-axis of the resulting plot.
ylab	Label for the y-axis of the resulting plot.
...	Additional arguments to be passed to either plot or arrows.

Value

Returns a list with the following components (the exact make up is dependent on the value of system):

add	As per input.
arrow.head	As per input.
arrow.type	As per input.
col	As per input, but with possible editing if a character vector of the wrong length was supplied.
deriv	As per input.
dx	A numeric 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 numeric 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.
frac	As per input.
parameters	As per input.
points	As per input.
system	As per input.
x	A numeric 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.
xlab	As per input.
xlim	As per input.
y	A numeric 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.
ylab	As per input.
ylim	As per input.

Author(s)

Michael J Grayling

See Also

arrows, plot

Examples

# Plot the flow field, nullclines and several trajectories for the
# one-dimensional autonomous ODE system logistic
logistic_flowField  <- flowField(logistic,
                                 xlim       = c(0, 5),
                                 ylim       = c(-1, 3),
                                 parameters = c(1, 2),
                                 points     = 21,
                                 system     = "one.dim",
                                 add        = FALSE)
logistic_nullclines <- nullclines(logistic,
                                  xlim       = c(0, 5),
                                  ylim       = c(-1, 3),
                                  parameters = c(1, 2),
                                  system     = "one.dim")
logistic_trajectory <- trajectory(logistic,
                                  y0         = c(-0.5, 0.5, 1.5, 2.5),
                                  tlim       = c(0, 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,
                                       xlim       = c(-7, 7),
                                       ylim       = c(-7, 7),
                                       parameters = 5,
                                       points     = 19,
                                       add        = FALSE)
y0                        <- matrix(c(0, 1, 0, 4, -6, 1, 5, 0.5, 0, -3),
                                    5, 2, byrow = TRUE)

simplePendulum_nullclines <- nullclines(simplePendulum,
                                        xlim       = c(-7, 7),
                                        ylim       = c(-7, 7),
                                        parameters = 5,
                                        points     = 500)

simplePendulum_trajectory <- trajectory(simplePendulum,
                                        y0         = y0,
                                        tlim       = c(0, 10),
                                        parameters = 5)

phaseR documentation built on Sept. 2, 2022, 5:07 p.m.