Periodic Oscillations for Nonmonotonic Smooth Negative Feedback Circuits

DOI10.1137/15M1033368zbMath1336.34061OpenAlexW2296198700MaRDI QIDQ2790859

Jean-Luc Gouzé, Camille Poignard, Madalena Chaves

Publication date: 8 March 2016

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

Full work available at URL: https://doi.org/10.1137/15m1033368

zbMATH Keywords

Poincaré mapsperiodic oscillationspiecewise linear systemsnegative feedback circuits

Mathematics Subject Classification ID

Feedback control (93B52) Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Neural networks for/in biological studies, artificial life and related topics (92B20) Applications of operator theory to differential and integral equations (47N20) Discontinuous ordinary differential equations (34A36)

Related Items

Qualitative Behavior of a Metabolic Pathway with Hybrid Feedback, A Stability Result for Periodic Solutions of Nonmonotonic Smooth Negative Feedback Systems, Quasimonotone random and stochastic functional differential equations with applications, Analysis of a genetic-metabolic oscillator with piecewise linear models, State-dependent effective interactions in oscillator networks through coupling functions with dead zones

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems
• On the existence of oscillatory solutions in negative feedback cellular control processes
• Existence of periodic solutions for negative feedback cellular control systems
• On the uniqueness and global asymptotic stability of periodic solutions for a third order system
• Stable oscillations in mathematical models of biological control systems
• Structure of the global attractor of cyclic feedback systems
• Comparing different ODE modelling approaches for gene regulatory networks
• The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model
• Periodic orbits of competitive and cooperative systems
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
• Piecewise linear and Boolean models of chemical reaction networks
• Structural principles for periodic orbits in Glass networks
• Piecewise-linear models of genetic regulatory networks: equilibria and their stability
• Hierarchy of models: From qualitative to quantitative analysis of circadian rhythms in cyanobacteria
• Cyclic feedback systems
• Periodic solutions in systems of piecewise- linear differential equations
• Limit cycles in piecewise-affine gene network models with multiple interaction loops
• Oscillations in Monotone Systems with a Negative Feedback
• Analysis of continuous-time switching networks