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Andronov-Hopf bifurcation of higher codimensions in a Liènard system
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.
Global region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of exchange of stability
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.