We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limit cycles can bifurcate from any center or focus at the origin of the system.
COBISS.SI-ID: 17613832
In this paper, we obtain the necessary and sufficient conditions for centers for a cubic planar system with Z2-symmetry studied by Yu and Han [2004]. We also give an example of such a system with 12 limit cycles of "real" (relatively large) size.
COBISS.SI-ID: 66719233
In this paper we propose an efficient computational approach to find systems with a first integral within some families of polynomial systems of ordinary differential equations in the case when the matrix of the linear approximation has one zero eigenvalue while the other eigenvalues have negative real parts. We apply it to find conditions for the existence of first integrals for a three-dimensional system involving cubic polynomials.
COBISS.SI-ID: 17759752
We study the level spacing distribution in the classically mixed-type quantum systems, exhibiting regular motion on invariant tori for some initial conditions and chaotic motion for the complementary initial conditions. In the asymptotic regime of the sufficiently deep semiclassical limit (sufficiently small effective Planck constant) the Berry and Robnik (1984) picture applies. which is very well established. We present a new quasi-universal semiempirical theory of the level spacing distribution in a regime, which includes the dynamical localization and the tunneling effects.
COBISS.SI-ID: 64947713
We investigate phenomenologically viable four- and five-stack MSSM D-brane quivers which exhibit realistic fermion mass hierarchies. In our analysis, the mass hierarchies arise either from higher order terms containing the VEV's of SM singlets or from D-instanton effects, where the latter utilizes either family splitting or a factorizable Yukawa matrix. We present a five-stack setup which overcomes all of the involved problems and exhibits three different mass scales for the up-quarks, down-quarks and electrons.
COBISS.SI-ID: 65740801