Mathematical analysis of a biochemical oscillator with delay

摘要: In this work we analyze a nonlinear delay differential equation (DDE) model with negative feedback and constant time delay. The is constructed from previously studied biochemical reaction network of gene transcription protein synthesis. Linear analysis the associated DDE gives critical beyond which periodic motion born in Hopf bifurcation. method multiple scales then used to system obtain expressions for amplitude frequency oscillation as function parameters. We use our closed form analytical study importance well-balanced ratio between synthesis degradation rates existence solutions. show that theoretical results are agreement numerical simulations experimental evidence found biological literature.