Many fracture branches are generated during hydraulic fracturing to form complex fracture networks and the majority of the gas in the unstimulated region (USR) is left unexploited. Traditional models usually overlook the key effect of bifurcating fracture morphology on gas production from hydraulically stimulated shale formation. Understanding the interaction behavior between the matrix system and the bifurcating fractures is important for exploiting shale reservoirs. In this regard, a modified quadruple-domain model with both the stimulated region (SR) and the USR, is established. The SR contains the bifurcating hydraulic fractures (BHF) which are captured by the Lindenmayer system (L-system) algorithm based on the coupling with microseismic events. Meanwhile, the effects of single layer and multiple layer sorption on gas transport are included in the new dynamic permeability equation. The model is validated against results from the experiment, field data, and numerical simulations. The results demonstrate that the initial axiom, bifurcating distance, deviation angle, and number of iterations have a significant influence on the morphology of the BHF and subsequently control its growth leading to complex network. BHF complexity, natural fracture geometry, and the amount of sorption gas simultaneously determine the flow behavior and cumulative production performance.