Quasi-Stable Structures in Circular Gene Networks

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 parame...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2018-05, Vol.58 (5), p.659-679
Main Authors: Glyzin, S. D., Kolesov, A. Yu, Rozov, N. Kh
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Differential equations
Mathematics
Mathematics and Statistics
Motion stability
Multipliers
Ordinary differential equations
Traveling waves
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518050093