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 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.


mathematical model circular gene network repressilator traveling wave asymptotics quasi-stability quasi-buffer phenomenon system of ordinary differential equations periodic solutions 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • S. D. Glyzin
    • 1
    • 2
  • A. Yu. Kolesov
    • 1
  • N. Kh. Rozov
    • 3
  1. 1.Faculty of MathematicsYaroslavl State UniversityYaroslavlRussia
  2. 2.Scientific Center in ChernogolovkaRussian Academy of SciencesChernogolovkaRussia
  3. 3.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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