Searches for an equilibium point of a system, taking the starting point of the search as a user specified point. 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 = c("x", "y"))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 guide.
The starting point of the search. In the case of a one dimensional system, this should be a single number indicating the location of the dependent variable initially. In the case of a two dimensional system, this should be a vector of length two reflecting the location of the two dependent variables initially. Alternatively this can be left blank and the user can use locator to specify initial condition on a plot. Defaults to NULL.
Parameters of the ODE system, to be passed to deriv. Supplied as a 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.
State names for ode functions that do not use positional states
Returns a list with the following components (the exact make up is dependent upon the value of system):
The classification of the identified equilibrium point.
In the two dimensional system case, value of the Jacobians 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 T^2 - 4*Delta.
In the two dimensional system case, the value of the Jacobians eigenvalues at the equilibrium point.
In the two dimensional system case, the value of the Jacobians 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 Jacobians trace at the equilibrium point.
As per input.
As per input.
The location of the identified equilibrium point.