Linear Stability Analysis of Multiparameter Dynamical Systems via a Numerical-Perturbation Approach

"A numerical-perturbation method, based on eigenvalue sensitivity analysis, is developed that is able to build up linear stability diagrams of multiparameter dynamical systems. The algorithm furnishes the critical combinations of parameters causing multiple bifurcations of static, dynamical, or mixed types. Moreover, it determines the manifolds in the parameter space on which simple bifurcations take place. Although the method is general, it is illustrated here for codimension-2 bifurcations only, sufficient for highlighting the underlying ideas."