drawManifolds: Stable and unstable manifolds In mjg211/phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

Description

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.

Usage

 ```1 2 3``` ```drawManifolds(deriv, y0 = NULL, parameters = NULL, tstep = 0.1, tend = 100, col = c("green", "red"), add.legend = TRUE, state.names = c("x", "y"), ...) ```

Arguments

 `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 `ode`. `y0` 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` 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`. `tstep` 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`. `tend` The final time of the numerical integration performed to identify the manifolds. `col` 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")`. `add.legend` Logical. If `TRUE`, a legend is added to the plots. Defaults to `TRUE`. `state.names` The state names for `ode` functions that do not use positional states. `...` Additional arguments to be passed to plot.

Value

Returns a `list` with the following components:

 `add.legend` As per input. `col` As per input, but with possible editing if a `character` `vector` of the wrong `length` was supplied. `deriv` As per input. `parameters` As per input. `stable.1` A `numeric` `matrix` whose columns are the numerically computed values of the dependent variables for part of the stable manifold. `stable.2` A `numeric` `matrix` whose columns are the numerically computed values of the dependent variables for part of the stable manifold. `tend` As per input. `unstable.1` A `numeric` `matrix` whose columns are the numerically computed values of the dependent variables for part of the unstable manifold. `unstable.2` A `numeric` `matrix` whose columns are the numerically computed values of the dependent variables for part of the unstable manifold. `y0` As per input. `ystar` Location of the identified equilibrium point.

Author(s)

Michael J Grayling, Stephen P Ellner, John M Guckenheimer

mjg211/phaseR documentation built on Oct. 11, 2019, 9:52 p.m.