title: Cellular control models with linked positive and negative feedback and delays. II. Linear analysis and local stability.
abstract: An analysis of local behavior is made of two nonlinear models which incorporate both an induction or positive feedback control mechanism and a repression or negative feedback control mechanism. The systems of differential equations with delays are linearized about their equilibria. The related characteristic equations which are exponential polynomials are studied to determine the local stability of the models. Computer studies are included to show the range of stability for different parameter values, and the biological significance is discussed briefly.
mesh_terms: D003201:Computers; D004926:Escherichia coli / Q000235:genetics* / Q000378:metabolism; D005246:Feedback; D007763:Lac Operon; D007785:Lactose / Q000378:metabolism; D008433:Mathematics; D008957:Models, Genetic; D012097:Repressor Proteins / Q000378:metabolism
chemical_list: D012097:Repressor Proteins; C001970:allolactose; D007785:Lactose