Hopf bifurcation from infinity for planar control systems (Q1365662)

Symmetric, piecewise linear two-dimensional systems are shown to exhibit Hopf bifurcation from infinity at certain parameter values. After some linear coordinate transformations, yielding a simpler normal form for the piecewise linear system, a coordinate inversion is applied which maps infinity to the origin. Using polar coordinates the leading expansion of a one-dimensional Poincaré map is computed in a small neighborhood of the origin, which shows the transcritical bifurcation of a nontrivial fixed point from the origin, corresponding to a large periodic solution in the original system. Due to the nonsmooth system the Poincaré map must be calculated in pieces.