Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points
This interesting paper exploits group theoretical methods to discuss bifurcation phenomena of a system of ordinary differential equations of the form \((1)\quad \dot x=g(x,\lambda)\) satisfying following condition \((2)\quad g(\gamma x,\lambda)=\gamma g(x,\lambda),\) \(\gamma\in \Gamma\). Here \(\gamma\) is an orthogonal matrix from certain group of \(N\times N\) matrices \(\Gamma\). These matrices are interpreted as some symmetries. The first part of the paper consists of a theoretical background and contains several group theory results especially proved for further applications to the investigated bifurcation problem. The application of these results enables one to detect, to classify, and to compute the bifurcation branches of solutions of (1), (2) for a large class of equations. Examples are from applications to chemical problems.
scientific article; zbMATH DE number 4111941
scientific article