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

DOI10.1016/0307-904X(89)90203-5zbMath0697.92013OpenAlexW2071875656MaRDI QIDQ912024

N. E. Zubov

Publication date: 1989

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0307-904x(89)90203-5

zbMATH Keywords

translationtranscriptionsupercritical Hopf bifurcationembryogenesisembryonic developmentPoincaré normal formbiological oscillationscentral manifold theoremepigenetic mechanismglobally stable limit cyclenonlinear multiple-loop negative- feedback control network modelunstable local equilibrium

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear systems in control theory (93C10) Control/observation systems governed by ordinary differential equations (93C15) Physiological, cellular and medical topics (92Cxx)

Cites Work

• Pattern formation and morphogenesis: A reaction-diffusion model
• Applications of centre manifold theory
• On the existence of oscillatory solutions in negative feedback cellular control processes
• Bifurcation of periodic orbits in a chemical reaction problem
• The qualitative dynamics of a class of biochemical control circuits
• Stability properties of neural and cellular control systems
• Existence of periodic solutions for negative feedback cellular control systems
• Mathematical aspects of periodic catatonic schizophrenia
• A global stability criterion for simple control loops
• Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks
• Model for the epigenetic mechanism during embryogenesis: a study of oscillations in a multiple-loop biochemical control network
• Some Mathematics of Biological Oscillations
• Hypergraphic Functions and Bifurcations in Recurrence Relations
• Global asymptotic stability of certain models for protein synthesis and repression
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
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