Periodic Trajectories and Andronov-Hopf Bifurcations in Models of Gene Networks
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Multistability is an important property of the gene network functioning. The estimate of possible numbers of limit cycles and stationary points of gene networks with various types of regulations is a fundamental problem of the applied mathematics, We prove existence of limit cycles for four classes of the gene network models where the control of protein concentrations is realized at the level of regulation of their stability. We show that the change in regulation from the stage of gene expression activation to the stage of degradation of the synthesis products does not affect the dynamical properties of the gene networks under consideration.
Key wordsDynamical systems Andronov-Hopf bifurcation fixed point theorem negative feedback regulation of degradation and synthesis of mRNA and proteins
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