In any gene regulatory network (GRN), the complex interactions occurring amongst transcription factors and target genes can be either instantaneousxe2x80x89or time-delayed. However, many existing modeling approaches currently applied for inferring GRNs are unable to represent both these interactions simultaneously. As a result, all these approaches cannot detect important interactions of the other type. S-System model, a differential equation based approach which has been increasingly applied for modeling GRNs, also suffers from this limitation. In fact, all S-System based existing modeling approaches have been designed to capture onlyxe2x80x89instantaneous interactions, and are unable to infer time-delayed interactions.