R/phaseR.R

In mjg211/phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

#' Phase plane analysis of one- and two-dimensional autonomous ODE systems
#'
#' phaseR is an R package for the qualitative analysis of one- and
#' two-dimensional autonomous ODE systems, using phase plane methods. Programs
#' are available to identify and classify equilibrium points, plot the direction
#' field, and plot trajectories for multiple initial conditions. In the
#' one-dimensional case, a program is also available to plot the phase portrait.
#' Whilst in the two-dimensional case, additionally programs are available to
#' plot nullclines and stable/unstable manifolds of saddle points. Many example
#' systems are provided for the user.
#'
#' \tabular{ll}{Package: \tab phaseR\cr Type: \tab Package\cr Version: \tab
#' 2.1\cr Date: \tab 2019-31-05\cr License: \tab GNU GPLv3\cr}
#' The package contains nine main functions for performing phase plane analyses:
#' \itemize{
#' \item \code{\link{drawManifolds}}: Draws the stable and unstable manifolds
#' of a saddle point in a two dimensional autonomous ODE system.
#' \item \code{\link{findEquilibrium}}: Identifies a nearby equilibrium point of
#' an autonomous ODE system based on a specified starting point.
#' \item \code{\link{flowField}}: Plots the flow or velocity field of a one- or
#' two-dimensional autonomous ODE system.
#' \item \code{\link{nullclines}}: Plots the nullclines of a two-dimensional
#' autonomous ODE system.
#' \item \code{\link{numericalSolution}}: Numerically solves a two-dimensional
#' autonomous ODE system in order to plot the two dependent variables against
#' the independent variable.
#' \item \code{\link{phasePlaneAnalysis}}: Provides a simple means of performing
#' a phase plane analysis by typing only numbers in to the command line.
#' \item \code{\link{phasePortrait}}: Plots the phase portrait of a
#' one-dimensional autonomous ODE system, for use in classifying equilibria.
#' \item \code{\link{stability}}: Performs stability, or perturbation, analysis
#' in order to classify equilibria.
#' \item \code{\link{trajectory}}: Numerically solves a one- or two-dimensional
#' ODE system to plot trajectories in the phase plane.}
#'
#' In addition, the package contains over 25 derivative functions for example
#' systems. Links to these can be found in the package index.
#'
#' An accompanying vignette containing further information, examples, and
#' exercises, can also be accessed with
#' \code{vignette("introduction", package = "phaseR")}.
#'
#' This package makes use of the \code{\link[deSolve]{ode}} function in the
#' package \code{\link[deSolve]{deSolve}}.
#'
#' @name phaseR-package
#' @aliases phaseR-package phaseR
#' @docType package
#' @author Michael J Grayling (michael.grayling@@ncl.ac.uk)
#'
#' Contributors: Gerhard Burger, Tomas Capretto, Stepehn P Ellner, John M
#' Guckenheimer
#'
#' @import graphics
#' @importFrom stats setNames
#' @importFrom deSolve ode
NULL

#' A function such that we can apply DRY in param documentation
#' @param state.names The state names for \code{\link[deSolve]{ode}} functions
#' that do not use positional states.
.paramDummy <- function(state.names) {}