Plots the stable and unstable manifolds of a saddle point. A search procedure is utilised to identify an equilibrium point, and if it is a saddle then its manifolds are added to the plot.
drawManifolds(deriv, y0 = NULL, parameters = NULL, tstep = 0.1,
tend = 100, col = c("green", "red"), add.legend = TRUE,
state.names = c("x", "y"), ...)Returns a list with the following components:
As per input.
As per input, but with possible editing if a
character vector of the wrong
length was supplied.
As per input.
As per input.
A numeric matrix
whose columns are the numerically computed values of the dependent variables
for part of the stable manifold.
A numeric matrix
whose columns are the numerically computed values of the dependent variables
for part of the stable manifold.
As per input.
A numeric matrix
whose columns are the numerically computed values of the dependent variables
for part of the unstable manifold.
A numeric matrix
whose columns are the numerically computed values of the dependent variables
for part of the unstable manifold.
As per input.
Location of the identified equilibrium point.
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 ode.
The initial point from which a saddle will be searched for. This
can either be a numeric vector of
length two, reflecting the location of the two
dependent variables, or alternatively this can be specified as
NULL, and then locator can be
used to specify the initial point on a plot. Defaults to
NULL.
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.
The step length of the independent variable, used in numerical
integration. Decreasing the absolute magnitude of tstep theoretically
makes the numerical integration more accurate, but increases computation
time. Defaults to 0.01.
The final time of the numerical integration performed to identify the manifolds.
Sets the colours used for the stable and unstable manifolds.
Should be a character vector of
length two. Will be reset accordingly if it is of the
wrong length. Defaults to c("green", "red").
Logical. If TRUE, a legend is added to the plots.
Defaults to TRUE.
The state names for ode functions
that do not use positional states.
Additional arguments to be passed to plot.
Michael J Grayling, Stephen P Ellner, John M Guckenheimer