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In this paper, we derive an analytic criterion for the existence of periodic oscillations in cyclic gene regulatory networks where each protein represses another gene expression in a cyclic way. We analyze local instability properties of large-scale cyclic gene regulatory networks based on the result which shows that local instability of an equilibrium point globally guarantees the existence of periodic...
This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincare??-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability...
This paper studies analytic robust stability criteria for large-scale cyclic gene-protein regulatory network systems with unstructured or parametric uncertainties. We first consider a class of gene expressions, which is described as uncertain Linear Transcription-Translation Models (LTTMs) with not only feedback loops from translation products to transcription but also degradation properties of proteins...
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