Some modified Michaelis–Menten equations having stable closed trajectories

DOI10.1017/S0308210500027815zbMath0652.34036OpenAlexW2052396251MaRDI QIDQ3797522

Russell A. Smith

Publication date: 1988

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500027815

zbMATH Keywords

chaoscritical pointPoincaré-Bendixson theoryclosed trajectorycellular biochemical reactionsglobal convergence of solutions

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) General biology and biomathematics (92B05) Dynamical systems and ergodic theory (37-XX)

Related Items (3)

Dynamics of the modified Michaelis--Menten system ⋮ Method of ``transition into space of derivatives: 40 years of evolution ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Massera's convergence theorem for periodic nonlinear differential equations
• Orbital stability for ordinary differential equations
• On the existence, uniqueness and global asymptotic stability of the periodic solution of the modified Michaelis Menten mechanism
• On the uniqueness and global asymptotic stability of periodic solutions for a third order system
• Certain differential equations have only isolated periodic orbits
• Some applications of Hausdorff dimension inequalities for ordinary differential equations
• Existence of periodic orbits of autonomous ordinary differential equations

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