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Continuation of codimension-2 equilibrium bifurcations in CONTENT. (English)
Doedel, Eusebius (ed.) et al., Numerical methods for bifurcation problems and large-scale dynamical systems. Based on two workshops held as part of the 1997-1998 IMA academic year on emerging applications of dynamical systems. New York, NY: Springer. IMA Vol. Math. Appl. 119, 163-184 (2000).
From the introduction: We consider a dynamical system depending on parameters, $$\dot u= F(u,α),\quad F: {\bbfR}^n\times {\bbfR}^m\to {\bbfR}^n,\tag 1$$ and its numerical study using CONTENT, an interactive software environment developed by Yu. A. Kuznetsov and V. V. Levitin. CONTENT can detect, compute and continue codimension-1 bifurcations of the solutions to the equilibrium equations $$F(u, α)= 0\tag 2$$ associated with (1). We discuss recent extensions to CONTENT to compute and continue all codimension-2 bifurcations of the solutions to (2).