MOTIVATION: Cell fate transitions are common in many developmental processes. Therefore, identifying the mechanisms behind them is crucial. Traditionally, due to complexity of networks and existence of plenty of kinetic parameters, dynamical analysis of biomolecular networks can only be performed by simultaneously perturbing a small number of parameters. Although many efforts have focused on how cell states change under specific perturbations, conversely, how to infer parametric conditions underlying distinct cell fates by systematic perturbations is less clear and needs to be further investigated. RESULTS: In this article, we present a general computational method by integrating systematic perturbations, unsupervised clustering, principal component analysis, and fitting analysis. The method can be used to to construct maps between distinct cell fates and parametric conditions by systematic perturbations. In particular, there are no needs of accurate parameter measurements and occurrence of bifurcations to establish the maps. To validate feasibility and inference performance of the method, we use toggle switch, inner cell mass, and epithelial mesenchymal transition as model systems to show how the maps are constructed and how system parameters encode essential information on cell fates. The maps tell us how systematic perturbations drive cell fate decisions and transitions, and allow us to purposefully predict, manipulate, and even control cell states. The approach is especially helpful in understanding crucial roles of certain parameter combinations during fate transitions. We hope that the approach can provide us valuable information on parametric or perturbation conditions so some specific targets, e.g. directional differentiation, can be realized. AVAILABILITY AND IMPLEMENTATION: No public data are used. The data we used are generated by randomly chosen values of model parameters in certain ranges, and the corresponding parameters are already attached in supplementary materials.