EXISTENCE OF LIMIT CYCLES IN THE REPRESSILATOR EQUATIONS

DOI10.1142/S0218127409025237zbMath1183.34063OpenAlexW1991731474MaRDI QIDQ5306405

Olguta Buse, Alexey S. Kuznetsov, Rodrigo A. Pérez

Publication date: 9 April 2010

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127409025237

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) Qualitative investigation and simulation of ordinary differential equation models (34C60) Systems biology, networks (92C42)

Related Items (13)

Cyclic feedback systems with quorum sensing coupling ⋮ Buffering in cyclic gene networks ⋮ Existence and stability of the relaxation cycle in a mathematical repressilator model ⋮ Quasi-stable structures in circular gene networks ⋮ Families of periodic orbits: closed 1-forms and global continuability ⋮ Mathematics of the genome ⋮ On a mathematical model of a repressilator ⋮ Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays ⋮ Unnamed Item ⋮ Cyclic negative feedback systems: what is the chance of oscillation? ⋮ An approach to modeling artificial gene networks ⋮ Oscillations in well-mixed, deterministic feedback systems: beyond ring oscillators ⋮ Hopf bifurcation in the full repressilator equations

Cites Work

• Unnamed Item
• Designer gene networks: Towards fundamental cellular control
• Synchrony in a Population of Hysteresis-Based Genetic Oscillators

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