Inspired by various astrophysical phenomenons, it was suggested that pulsar-like compact stars may in fact be strangeon stars, comprised entirely of strangeons (quark-clusters with three-light-flavor symmetry) and a small amount of electrons. To examine such possibilities, in this work we propose a linked bag model, which can be adopted for strong condensed matter in both 2-flavoured (nucleons) and 3-flavoured (hyperons, strangeons, etc.) scenarios. The model parameters are calibrated to reproduce the saturation properties of nuclear matter, which are later applied to hyperonic matter and strangeon matter. The obtained energy per baryon of strangeon matter is reduced if we adopt larger quark numbers inside a strangeon, which stiffens the equation of state and consequently increases the maximum mass of strangeon stars. In a large parameter space, the maximum mass and tidal deformability of strangeon stars predicted in the linked bag model are consistent with the current astrophysical constraints. It is found that the maximum mass of strangeon stars can be as large as $sim 2.5M_odot$, while the tidal deformability of a $1.4M_odot$ strangeon star lies in the range of $180lesssim Lambda_{1.4} lesssim 340$. More refined theoretical efforts as well as observational tests to these results are necessary in the future.
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