Quasi-Stable Structures in Circular Gene Networks


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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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