Bull Math Biol DOI 10.1007/s11538-012-9733-1 ORIGINAL ARTICLE Modeling of Hysteresis in Gene Regulatory Networks J. Hu · K.R. Qin · C. Xiang · T.H. Lee Received: 15 July 2011 / Accepted: 30 April 2012 © Society for Mathematical Biology 2012 Abstract Hysteresis, observed in many gene regulatory networks, has a pivotal im- pact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc–Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical proper- ties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc–Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hys- teresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the poten- tial to be a unified framework for modeling hysteresis in gene regulatory networks J. Hu · C. Xiang ( ) · T.H. Lee Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore e-mail: elexc@nus.edu.sg J. Hu · T.H. Lee Graduate School for Integrative Science and Engineering, National University of Singapore, Singapore, Singapore K.R. Qin Department of Biomedical Engineering, Dalian University of Technology, Dalian 116024, China