The study of prestellar cores is critical as they set the initial conditions in star formation and determine the final mass of the stellar object. To date, several hypotheses are describing their gravitational collapse. We perform detailed line analysis and modelling of H$_{2}$D$^{+}$ 110 -111 and N$_{2}$H$^{+}$ 4-3 emission at 372 GHz, using 2x2 maps (JCMT). Our goal is to test the most prominent dynamical models by comparing the modelled gas kinematics and spatial distribution (H$_{2}$D$^{+}$ and N$_{2}$H$^{+}$) with observations towards four prestellar (L1544, L183, L694-2, L1517B) and one protostellar core (L1521f). We perform a detailed non-LTE radiative transfer modelling using RATRAN, where we compare the predicted spatial distribution and line profiles of H$_{2}$D$^{+}$ and N$_{2}$H$^{+}$ with observations towards all cores. To do so, we adopt the physical structure for each core predicted by three different dynamical models taken from literature: Quasi-Equilibrium Bonnor-Ebert Sphere (QE-BES), Singular Isothermal Sphere (SIS), and Larson-Penston (LP) flow. Our analysis provides an updated picture of the physical structure of prestellar cores. We find that the SIS model can be clearly excluded in explaining the gas emission towards the cores, but a larger sample is required to differentiate clearly between the LP flow, the QE-BES and the static models. All models of collapse underestimate the intensity of the gas emission by up to several factors towards the only protostellar core in our sample, indicating that different dynamics take place in different evolutionary core stages. If the LP model is confirmed towards a larger sample of prestellar cores, it would indicate that they may form by compression or accretion of gas from larger scales. If the QE-BES model is confirmed, it means that quasi hydrostatic cores can exist within turbulent ISM.
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