BioND — Dynamics of Biological Networks

Triangulation: A tool for calculating bifurcation surfaces

About the class

The triangulation c++ class utilizes an algorithm for calculating bifurcation surfaces [1] and is an effcient tool to calculate hopf- and fold-bifurcation surfaces of an input function. It provides mesh triangles for the graphical representations of the surfaces.

Getting started

A basic example

The triangulation class provides a basic test function for getting started. Just download the triangulation.zip and extract the files. Please adapt the make file and compile the class. Running the programm will compute the Hopf bifurcation surface and provide mesh triangles for a graphical representation in the result folder.

Own functions

To include your own functions you have to adapt the bisurf.cpp file. There, the function evalFunc() takes a vector of coordinates as input and returns the function value as output. Please replace the test function by your function, e.g. a test function for a Hopf bifurcation; bifurcation surfaces will be calculated for this function. Different options for the triangulation class can be adjusted in the file triangulation.dat.

Refrences

[1] C.T. Kelley Solving Nonlinear Equations with Newton's Method, Society for Industrial and Applied Mathematics (1987)

Files