A Stability Result for Periodic Solutions of Nonmonotonic Smooth Negative Feedback Systems

DOI10.1137/17M1141205zbMath1392.37097OpenAlexW2795471767WikidataQ130032687 ScholiaQ130032687MaRDI QIDQ4571167

Madalena Chaves, Jean-Luc Gouzé, Camille Poignard

Publication date: 6 July 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1141205

zbMATH Keywords

asymptotic stabilitymonodromy matrixperiodic oscillationpiecewise linear systemnegative feedback circuitperiodic orbits of vector fields and flows

Mathematics Subject Classification ID

Feedback control (93B52) Asymptotic stability in control theory (93D20) Stability of solutions to ordinary differential equations (34D20) Dynamical systems in control (37N35) Periodic orbits of vector fields and flows (37C27)

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Qualitative Behavior of a Metabolic Pathway with Hybrid Feedback, Quasimonotone random and stochastic functional differential equations with applications, State-dependent effective interactions in oscillator networks through coupling functions with dead zones

Cites Work

• The Poincaré-Bendixson theorem for monotone cyclic feedback systems
• Existence of periodic solutions for negative feedback cellular control systems
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
• Piecewise-linear models of genetic regulatory networks: equilibria and their stability
• Periodic Oscillations for Nonmonotonic Smooth Negative Feedback Circuits
• Oscillations in Monotone Systems with a Negative Feedback
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