Description Usage Arguments Value Note Author(s) See Also Examples
Plots nullclines for twodimensional autonomous ODE systems. Can also be used to plot horizontal lines at equilibrium points for onedimensional autonomous ODE systems.
1 2 3 4 
deriv 
A function computing the derivative at a point for the ODE
system to be analysed. Discussion of the required structure 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 at which derivatives are computed;

col 
In the case of a twodimensional system, sets the colours used
for the x and ynullclines. In the case of a onedimensional system, sets
the colour of the lines plotted horizontally along the equilibria. Should be
a 
add 
Logical. If 
add.legend 
Logical. If 
state.names 
The state names for 
... 
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. 
add.legend 
As per input. 
col 
As per input, but with possible editing if a

deriv 
As per input. 
dx 
A 
dy 
A 
parameters 
As per input. 
points 
As per input. 
system 
As per input. 
x 
A 
xlim 
As per input. 
y 
A 
ylim 
As per input. 
In order to ensure a nullcline is plotted, set xlim
and
ylim
strictly enclosing its location. For example, to ensure a
nullcline is plotted along x = 0, set ylim
to, e.g., begin at 1.
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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