Description Usage Arguments Value Author(s) See Also Examples
Plots the flow or velocity field for a one or twodimensional autonomous ODE system.
1 2 3 4 5 6  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], ...)

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 
xlim 
In the case of a twodimensional system, this sets the limits of
the first dependent variable in which gradient reflecting line segments
should be plotted. In the case of a onedimensional system, this sets the
limits of the independent variable in which these line segments should be
plotted. Should be a 
ylim 
In the case of a twodimensional system this sets the limits of
the second dependent variable in which gradient reflecting line segments
should be plotted. In the case of a onedimensional system, this sets the
limits of the dependent variable in which these line segments should be
plotted. Should be a 
parameters 
Parameters of the ODE system, to be passed to 
system 
Set to either 
points 
Sets the density of the line segments to be plotted;

col 
Sets the colour of the plotted line segments. Should be a

arrow.type 
Sets the type of line segments plotted. If set to

arrow.head 
Sets the length of the arrow heads. Passed to

frac 
Sets the fraction of the theoretical maximum length line
segments can take without overlapping, that they can actually attain. In
practice, 
add 
Logical. If 
state.names 
The state names for 
xlab 
Label for the xaxis of the resulting plot. 
ylab 
Label for the yaxis of the resulting plot. 
... 
Additional arguments to be passed to either

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

deriv 
As per input. 
dx 
A 
dy 
A 
frac 
As per input. 
parameters 
As per input. 
points 
As per input. 
system 
As per input. 
x 
A 
xlab 
As per input. 
xlim 
As per input. 
y 
A 
ylab 
As per input. 
ylim 
As per input. 
Michael J Grayling
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39  # Plot the flow field, nullclines and several trajectories for the
# onedimensional 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
# twodimensional 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)

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