Structural analysis, biological networks dynamics

We repeat these simple examples from earlier work since they form a major justification for the elaborations we report below, and if they are understood well, then much of what follows should be clear. The dynamics in the differential equations are in qualitative agreement with the dynamics in the synthetic genetic networks in E. coU. One important aspect of biology is to understand the ways in which the organization and structure of the control networks can be used to predict the dynamics. Thus, we would like to develop methods that could be used to predict the dynamic behaviors just demonstrated without integrating or carrying out the stability analysis of the differential equations. 

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