Quantitative analysis of the Hopf bifurcation in the Goodwin n- dimensional metabolic control system

DOI10.1007/BF00160189zbMath0732.92003WikidataQ52461668 ScholiaQ52461668MaRDI QIDQ809916

Giulia Treu, Sergio Invernizzi

Publication date: 1991

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

feedback controlpositive equilibriumbifurcation formulaedynamics of end-product inhibition of gene activityGoodwin systemHill coefficientHopf bifurcation of nontrivial periodic solutionsmetabolic control systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Biochemistry, molecular biology (92C40) Control problems involving ordinary differential equations (34H05)

Related Items (5)

Bifurcations for Goodwin model with three delays ⋮ Stability and Hopf bifurcation analysis on Goodwin model with three delays ⋮ Local Hopf bifurcation analysis and global existence of periodic solutions in a gene expression model with delays ⋮ Hopf bifurcation in an \(n\)-dimensional Goodwin model via multiple delays feedback ⋮ BIFURCATION CONTROL: THEORIES, METHODS, AND APPLICATIONS

Cites Work

• On lags and chaos in economic dynamic models
• Infinite-dimensional dynamical systems in mechanics and physics
• On the existence of oscillatory solutions in negative feedback cellular control processes
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• On the theory and application of the Hopf-Friedrich Bifurcation theory
• Existence of periodic solutions for negative feedback cellular control systems
• Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks
• Harmonic balance and the Hopf bifurcation
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