We solve numerically the Einstein-Klein-Gordon system with spherical symmetry, for a massive real scalar field endowed with a quartic self-interaction potential, and obtain the so-called $Phi^4$-oscillatons which is the short name for oscillating soliton stars. We analyze numerically the stability of such oscillatons, and study the influence of the quartic potential on the behavior of both, the stable (S-oscillatons) and unstable (U-oscillatons) cases under small and strong radial perturbations.
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