The complexity and nonlinear dynamics of patterning networks in development make modeling an important approach for the evaluation of the experimentally derived pattern formation mechanisms. As a rule, mechanistic models of patterning networks have large number of uncertain parameters; model analysis requires extensive computational searches of the parameter space. Analytical techniques can circumvent these difficulties and offer important insights into the networks' functional capabilities. Here, we present an asymptotic analysis of the multiple steady states and transitions between them in a mechanistic model of patterning events specifying the formation of a pair organ in Drosophila oogenesis. The model describes the interaction between the spatially nonuniform inductive signal and a network of spatially distributed feedback loops. Our approach dramatically reduces the complexity of the problem and provides an explicit analytical method for the construction and parametric analysis of the patterned states responsible for signaling. The analysis reveals a skeleton structure for the patterning capability of the considered regulatory module and demonstrates how a single regulatory network can be used to generate a variety of developmental patterns.