Searches for an equilibium point of a system, taking the starting point of the search as a user specified location. On identifying such a point, a classification is performed, and an informatively shaped point can be added to the plot.
findEquilibrium(
deriv,
y0 = NULL,
parameters = NULL,
system = "two.dim",
tol = 1e-16,
max.iter = 50,
h = 1e-06,
plot.it = FALSE,
summary = TRUE,
state.names = if (system == "two.dim") c("x", "y") else "y"
)Returns a list with the following components (the exact make up is
dependent on the value of system):
The classification of the identified equilibrium point.
In the two-dimensional system case, value of the Jacobian's determinant at the equilibrium point.
As per input.
In the one-dimensional system case, the value of the
discriminant used in perturbation analysis to assess stability. In the
two-dimensional system case, the value of tr^2 - 4*Delta.
In the two-dimensional system case, the value of the Jacobian's eigenvalues at the equilibrium point.
In the two-dimensional system case, the value of the Jacobian's eigenvectors at the equilibrium point.
In the two-dimensional system case, the Jacobian at the equilibrium point.
As per input.
As per input.
As per input.
As per input.
As per input.
As per input.
In the two-dimensional system case, the value of the Jacobian's trace at the equilibrium point.
As per input.
As per input.
The 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 starting point of the search. In the case of a one-dimensional
system, this should be a numeric
vector of length one indicating the
location of the dependent variable initially. In the case of a
two-dimensional system, this should be a numeric
vector of length two reflecting the
location of the two dependent variables initially. 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.
Set to either "one.dim" or "two.dim" to indicate
the type of system being analysed. Defaults to "two.dim".
The tolerance for the convergence of the search algorithm.
Defaults to 1e-16.
The maximum allowed number of iterations of the search
algorithm. Defaults to 50.
Step length used to approximate the derivative(s). Defaults to
1e-6.
Logical. If TRUE, a point is plotted at the identified
equilibrium point, with shape corresponding to its classification.
Set to either TRUE or FALSE to determine whether
a summary of the progress of the search procedure is returned. Defaults to
TRUE.
The state names for ode functions
that do not use positional states.
Michael J Grayling, Stephen P Ellner, John M Guckenheimer