Abstract: We consider the Shimizu-Morioka system, a special generalized Lorenz canonical form. Using techniques of elimination in the computation of algebraic varieties we obtain parameter dependent normal forms on a center manifold. Our computation shows that the maximal number of limit cycles produced from Hopf bifurcations is four and only even number of limit cycles can be bifurcated near the two equilibria because of -symmetry. Our parameter-dependent normal forms enable us to give parameter conditions for the cases of none, two and four limit cycles separately. Furthermore, considering exterior perturbations, we give conditions under which one or three limit cycles can be produced from Hopf bifurcations.
Seminarsko predavanje bo v torek 20. avgusta 2013 ob 17:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.