phaseR-package: Phase plane analysis of one- and two-dimensional autonomous...

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

Description

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.

Details

Package:	phaseR
Type:	Package
Version:	2.1
Date:	2019-31-05
License:	GNU GPLv3

The package contains nine main functions for performing phase plane analyses:

• drawManifolds: Draws the stable and unstable manifolds of a saddle point in a two dimensional autonomous ODE system.

• findEquilibrium: Identifies a nearby equilibrium point of an autonomous ODE system based on a specified starting point.

• flowField: Plots the flow or velocity field of a one- or two-dimensional autonomous ODE system.

• nullclines: Plots the nullclines of a two-dimensional autonomous ODE system.

• numericalSolution: Numerically solves a two-dimensional autonomous ODE system in order to plot the two dependent variables against the independent variable.

• phasePlaneAnalysis: Provides a simple means of performing a phase plane analysis by typing only numbers in to the command line.

• phasePortrait: Plots the phase portrait of a one-dimensional autonomous ODE system, for use in classifying equilibria.

• stability: Performs stability, or perturbation, analysis in order to classify equilibria.

• 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 vignette("introduction", package = "phaseR").

This package makes use of the ode function in the package deSolve.

Author(s)

Michael J Grayling ([e-mail])

Contributors: Gerhard Burger, Tomas Capretto, Stepehn P Ellner, John M Guckenheimer

mjg211/phaseR documentation built on Sept. 11, 2022, 6:26 p.m.