Quasi-Stable Structures in Circular Gene Networks
- Authors: Glyzin S.D.1,2, Kolesov A.Y.1, Rozov N.K.3
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Affiliations:
- Faculty of Mathematics
- Scientific Center in Chernogolovka
- Faculty of Mechanics and Mathematics
- Issue: Vol 58, No 5 (2018)
- Pages: 659-679
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/180204
- DOI: https://doi.org/10.1134/S0965542518050093
- ID: 180204
Cite item
Abstract
A new mathematical model is proposed for a circular gene network representing a system of unidirectionally coupled ordinary differential equations. The existence and stability of special periodic motions (traveling waves) for this system is studied. It is shown that, with a suitable choice of parameters and an increasing number m of equations in the system, the number of coexisting traveling waves increases indefinitely, but all of them (except for a single stable periodic solution for odd m) are quasistable. The quasi-stability of a cycle means that some of its multipliers are asymptotically close to the unit circle, while the other multipliers (except for a simple unit one) are less than unity in absolute value.
About the authors
S. D. Glyzin
Faculty of Mathematics; Scientific Center in Chernogolovka
Author for correspondence.
Email: glyzin@uniyar.ac.ru
Russian Federation, Yaroslavl, 150000; Chernogolovka, Moscow oblast, 142432
A. Yu. Kolesov
Faculty of Mathematics
Email: glyzin@uniyar.ac.ru
Russian Federation, Yaroslavl, 150000
N. Kh. Rozov
Faculty of Mechanics and Mathematics
Email: glyzin@uniyar.ac.ru
Russian Federation, Moscow, 119991
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