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- ItemAndronov-Hopf bifurcation of higher codimensions in a Liènard system(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Schneider, Klaus; Grin, AlexanderConsider 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.
- ItemGlobal region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of exchange of stability(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Butuzov, Valentin F.; Nefedov, Nikolai N.; Recke, Lutz; Schneider, KlausWe 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.