In this study, we have introduced a modern technique that can deal with a specific 4−dimensional network. In my opinion, this is not studied before. Such an approach will be feasible to address gene networks and answer the relevant biological questions. Theoretically, the analysis has been made and validated geometrically under the ambient of hypercube. A continuous ho-molog gives us information and based on that we can predict its behavioral dynamics. Moreover, we investigate the results in Matlab and express its behavior through figures. Numerical calculation of Poincaré maps is used to address new evidence of dynamics pointing to a new direction of research.