Our objective: Find limit cycles and analyze their stability in a hybrid modeling framework of gene regulatory networks [Cornillon et al. 2016] [Behaegel, Comet, Bernot, et al. 2016] [Behaegel, Comet, and Folschette 2017] which extends René Thomas' discrete modeling. Our idea: Extend Poincaré map to this hybrid framework. Our contribution: We search for potential cycles by abstracting the continuous trajectory into a succession of visited discrete domains. Then we introduce transition matrices and stable zones to analyze the concrete continuous dynamics and find the actual cycles that are stable.