Model for the epigenetic mechanism during embryogenesis: a study of oscillations in a multiple-loop biochemical control network

DOI10.1080/00207728808964070zbMath0664.92009OpenAlexW1992563375MaRDI QIDQ3815911

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Publication date: 1988

Published in: International Journal of Systems Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207728808964070

zbMATH Keywords

Lyapunov functionreduced systemsingular perturbationsHopf bifurcationcritical valuestranslationoscillatory propertiestranscriptionglobally stableembryonic developmentstability of limit cyclesNyquist diagramnormal transformationsBrujno's theoremmulti-loop feedback systemmultiple- loop control networkNyquist's stability criterionopen-loop transfer functionsTykhonov's theorem

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Application models in control theory (93C95) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Physiological, cellular and medical topics (92Cxx)

Related Items (1)

Oscillations in a multiple-loop negative-feedback control network model for transcription and translation during embryogenesis

Cites Work

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• A global stability criterion for simple control loops
• Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks
• Periodic solutions and asymptotic stability
• Some Mathematics of Biological Oscillations
• Regeneration Theory

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