Quasi-stable structures in circular gene networks

DOI10.1134/S0965542518050093zbMath1398.34066OpenAlexW2808499073MaRDI QIDQ1662564

S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov

Publication date: 20 August 2018

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542518050093

zbMATH Keywords

periodic solutionsasymptoticsmathematical modelsystem of ordinary differential equationstraveling wavequasi-stabilityrepressilatorcircular gene networkquasi-buffer phenomenon

Mathematics Subject Classification ID

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) Stability of solutions to ordinary differential equations (34D20) Periodic solutions to functional-differential equations (34K13) Qualitative investigation and simulation of ordinary differential equation models (34C60) Genetics and epigenetics (92D10) Singular perturbations for ordinary differential equations (34E15)

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Cites Work

• Existence and stability of the relaxation cycle in a mathematical repressilator model
• Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations
• Periodic solutions of travelling-wave type in circular gene networks
• The buffer phenomenon in ring-like chains of unidirectionally connected generators
• Relaxation self-oscillations in Hopfield networks with delay
• EXISTENCE OF LIMIT CYCLES IN THE REPRESSILATOR EQUATIONS
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