**Publication date:** Dec 2007

**Abstract:**

Assuming a resonant origin of the twin peak quasiperiodic oscillations

observed in the X-ray neutron star binary systems, we apply a genetic

algorithm method for selection of neutron star models. It was suggested

that pairs of kilohertz peaks in the X-ray Fourier power density spectra

of some neutron stars reflect a non-linear resonance between two modes

of accretion disk oscillations. We investigate this concept for a

specific neutron star source. Each neutron star model is characterized

by the equation of state (EOS), rotation frequency Ω and central energy

density rho_{c}. These determine the spacetime structure governing

geodesic motion and position dependent radial and vertical epicyclic

oscillations related to the stable circular geodesics. Particular kinds

of resonances (KR) between the oscillations with epicyclic frequencies,

or the frequencies derived from them, can take place at special

positions assigned ambiguously to the spacetime structure. The pairs of

resonant eigenfrequencies relevant to those positions are therefore

fully given by KR, rho_{c}, Ω, EOS and can be compared to the

observationally determined pairs of eigenfrequencies in order to

eliminate the unsatisfactory sets (KR, rho_{c}, Ω, EOS). For the

elimination we use the advanced genetic algorithm. Genetic algorithm

comes out from the method of natural selection when subjects with the

best adaptation to assigned conditions have most chances to survive. The

chosen genetic algorithm with sexual reproduction contains one

chromosome with restricted lifetime, uniform crossing and genes of type

3/3/5. For encryption of physical description (KR, rho_{c}, Ω, EOS) into

the chromosome we use the Gray code. As a fitness function we use

correspondence between the observed and calculated pairs of

eigenfrequencies.

**Authors:**

Urbanec, Martin; Stuchlík, Zdeněk; Török, Gabriel; Bakala, Pavel; Čermák, Petr;