This article is cited in 10 papers

Cycles in the odd-dimensional models of circular gene networks

V. P. Golubyatnikov, V. V. Ivanov

Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia

Abstract: The necessary and sufficient conditions are obtained for the existence of a cycle in an odd-dimensional nonlinear dynamical system that simulates the functioning of the simplest circular gene network. An invariant neighborhood of this cycle is described which is homeomorphic to a torus.

Keywords: block-linear autonomous system, phase portrait, circular gene network, fixed point of a monotonic mapping, cycle.

UDC: 514.745.82

Received: 28.07.2018

DOI: 10.17377/sibjim.2018.21.403

 English version: Journal of Applied and Industrial Mathematics, 2018, 12:4, 648–657

Bibliographic databases:

• 
• 
•