Rational maps associated with the Sigmoid Beverton-Holt model on the projective line over <inline-formula><tex-math id="M1">$ \mathbb{Q}_p $</tex-math></inline-formula>

We describe the dynamical structure of the $ p $-adic rational dynamical systems associated with the Sigmoid Beverton-Holt model on the projective line $ \mathbb{P}^1(\mathbb{Q}_p) $ over the field $ \mathbb{Q}_p $ of $ p $-adic numbers. Our methods are minimal decomposition of $ p $-adic polynomials with coefficients in $ \mathbb{Z}_p $ established by Fan and Liao and the chaotic description of $ p $-adic repellers of Fan, Liao, Wang and Zhou.