1. M.A. Al-Radhawi, D. Angeli, and E.D. Sontag. On structural contraction of biological interaction networks. SIAM J Applied Dynamical Systems, 2025. Note: Submitted. Preprint in: arXiv http://arxiv.org/abs/2307.13678.Keyword(s): contractions, contractive systems, matrix measures, logarithmic norms. Abstract:

   In previous work, we have developed an approach to understanding the long-term dynamics of classes of chemical reaction networks, based on rate-dependent Lyapunov functions. In this paper, we show that stronger notions of convergence can be established by proving contraction with respect to non-standard norms. This enables us to show that such networks entrain to periodic inputs. We illustrate our theory with examples from signaling pathways and genetic circuits.

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