2011, Schneider, Klaus, Grin, Alexander

Consider a polynominal Liènard system depending on three parameters itshape a, b, c   and with the following properties: (i) The origin is the unique equilibrium for all parameters. (ii) Ifitshape a crosses zero, then the origin changes its stability, and a limit cycle bifurcates from the euqilibrium. We inverstigate analytically this bifurcation in dependence on the parameters itshape b and itshape c and establish the existence of families of limit cycles of multiplicity one, two and three bifurcating from the origin.

2009, Butuzov, Valentin F., Nefedov, Nikolai N., Recke, Lutz, Schneider, Klaus

We consider a singularly perturbed parabolic differential equation in case that the degenerate equation has two intersecting roots. In a previous paper we presented conditions under which there exists an asymptotically stable periodic solution satisfying no-flux boundary conditions. In this note we characterize a set of initial functions belonging to the global region of attraction of that periodic solution.