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We perform an analysis of the Einstein-Skyrme cosmological model inBianchi-IX background. We analytically describe asymptotic regimes andsemi-analytically -- generic regimes. It appears that depending on the productof Newtonian constant $\kappa$ with Skyrme coupling $K$, in absence of thecosmological term there are three regimes possible -- recollapse with $\kK < 2$and two power-law regimes -- $\propto t^{1/2}$ for $\kK=2$ and $\propto t$ for$\kK > 2$. In presence of the positive cosmological term, power-law regimesturn to exponential (de Sitter) ones while recollapse regime turn toexponential if the value for $\Lambda$-term is sufficiently large, otherwisethe regime remains recollapse. Negative cosmological term leads to therecollapse regardless of $\kK$. All nonsingular regimes have the squashingcoefficient $a(t) \to 1$ at late times, which is associated with restoringsymmetry dynamics. Also all nonsingular regimes appear to be linearly stable --exponential solutions always while power-law for an open region of initialconditions.

Dynamics of gravitating hadron matter in Bianchi-IX cosmological model