Preface

This software package is developed for equilibrium and bifurcation analysis of systems of ordinary differential equations (ODEs). If you are not familiar with the bifurcation theory of continuous-time systems described in terms of ODEs the book by Kuznetsov (1995) is an excellent source to consult that I highly recommend. Many of the numerical procedures implemented in this package are taken from that book.

This package consists of two functions, called phaseplane() and bifurcation(), that both start up a shiny application (Chang et al. 2019). Shiny is a web application framework for R, which also allows to run an application on your local machine. I used shiny (Chang et al. 2019) and the related packages shinydashboard (Chang and Borges Ribeiro 2018) and shinydashboardPlus (Granjon 2019) to create a graphical user interface. Under the hood, I use the packages deSolve (Soetaert, Petzoldt, and Setzer 2010) for time integration of the ODEs and the package rootSolve (Soetaert 2009) as well as my own implementation of a root finding function for the numerical solution of equilibrium and bifurcation conditions.

The package is free software and released under the GNU General Public License without any warranty or even the implied warranty of merchantability or fitness for a particular purpose (the official statement of the GPL). If you are using the software for publications, you are kindly asked to credit this software package by a reference to this documentation and the website that hosts the software package, as these are currently the only sources to be referred to.

In case you encounter any problem with the software package, please first verify the problem is not in your own model-specific file, but indeed is a bug in the general software layer. If you are convinced it is a bug in my programming, send me an email with as accurate a description of the problem as possible. Do not not forget to include your model-specific file and details about how to trigger the problems. Any comments and feedback, both on the code and on the current manual is appreciated and will be considered carefully. In particular concrete comments, for example, explicit suggestions for textual changes in the manual and/or corrections of the mistakes (they are definitely there!) will be highly valued and acknowledged.

References

Chang, Winston, and Barbara Borges Ribeiro. 2018. Shinydashboard: Create Dashboards with ’Shiny’. https://CRAN.R-project.org/package=shinydashboard.
Chang, Winston, Joe Cheng, JJ Allaire, Yihui Xie, and Jonathan McPherson. 2019. Shiny: Web Application Framework for r. https://CRAN.R-project.org/package=shiny.
Granjon, David. 2019. shinydashboardPlus: Add More ’AdminLTE2’ Components to ’Shinydashboard’. https://CRAN.R-project.org/package=shinydashboardPlus.
Kuznetsov, Y A. 1995. Elements of applied bifurcation theory. Heidelberg: Springer-Verlag.
Soetaert, Karline. 2009. rootSolve: Nonlinear Root Finding, Equilibrium and Steady-State Analysis of Ordinary Differential Equations.
Soetaert, Karline, Thomas Petzoldt, and R. Woodrow Setzer. 2010. “Solving Differential Equations in R: Package deSolve.” Journal of Statistical Software 33 (9): 1–25. https://doi.org/10.18637/jss.v033.i09.