Hopf bifurcation in the full repressilator equations

DOI10.1002/mma.3158zbMath1322.34060OpenAlexW2055544900MaRDI QIDQ5259845

Jaume Llibre, Claudio A. Buzzi

Publication date: 29 June 2015

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/145362

zbMATH Keywords

limit cyclesrepressilatoroscillatory regulatory networks

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60)

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Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III ⋮ Synchrony patterns in gene regulatory networks

Cites Work

• Designer gene networks: Towards fundamental cellular control
• PREDICTING THE SYNCHRONIZATION OF A NETWORK OF ELECTRONIC REPRESSILATORS
• Synchrony in a Population of Hysteresis-Based Genetic Oscillators
• Transient dynamics around unstable periodic orbits in the generalized repressilator model
• EXISTENCE OF LIMIT CYCLES IN THE REPRESSILATOR EQUATIONS
• Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing

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