The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and expand upon the body of mathematical results pertaining to the theory of multiple equilibria in chemical reaction networks (CRNs), which has yielded surprising insights with minimal computational effort. Our central focus is a recent, cycle-based theorem by Gheorghe Craciun and Martin Feinberg, which is of significant interest in its own right and also serves, in a somewhat restated form, as the basis for a number of fruitful connections among related results.
Approximating Parameter Regions for Multistationarity and Multistability in Mass-Action Systems
Institute of Mathematical Sciences, University of the Philippines Los Baños（菲律宾大学洛斯巴尼奥斯分校数学科学研究所）；Data Science Program, College of Science, University of the Philippines Diliman（菲律宾大学迪利曼分校理学院数据科学项目）；Institute of Mathematics, University of the Philippines Diliman（菲律宾大学迪利曼分校数学研究所）
A mathematical framework to study organising principles in graphical representations of biochemical processes
University of Rostock（罗斯托克大学）；Christian-Albrechts-University（克里斯蒂安-阿尔布莱希特大学）；Leibniz-Institute for Food Systems Biology（莱布尼茨食品系统生物研究所）；Technical University of Munich（慕尼黑工业大学）；Stellenbosch Institute for Advanced Study（斯泰伦博斯高等研究院）
A flux-based approach for analyzing the disguised toric locus of reaction networks
Bolyai Institute, University of Szeged（博莱研究所，塞格德大学）；National Laboratory for Health Security, University of Szeged（国家健康安全实验室，塞格德大学）；Department of Mathematics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校数学系）；Department of Biomolecular Chemistry, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物分子化学系）；Max Planck Institute of Molecular Cell Biology and Genetics, Dresden（德累斯顿马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Department of Mathematics, University of Louisiana at Lafayette（路易斯安那大学拉斐特分校数学系）
