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.
Keywordsmathematical model circular gene network repressilator traveling wave asymptotics quasi-stability quasi-buffer phenomenon system of ordinary differential equations periodic solutions
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- 15.Yu. M. Romanovskii, N. V. Stepanova, and D. S. Chernavskii, Mathematical Modeling in Biophysics (Inst. Komp’yut. Issled., Moscow, 2003) [in Russian].Google Scholar