Quasi-Stable Structures in Circular Gene Networks |
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Authors: | S D Glyzin A Yu Kolesov N Kh Rozov |
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Institution: | 1.Faculty of Mathematics,Yaroslavl State University,Yaroslavl,Russia;2.Scientific Center in Chernogolovka,Russian Academy of Sciences,Chernogolovka,Russia;3.Faculty of Mechanics and Mathematics,Moscow State University,Moscow,Russia |
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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. |
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