Abstract

We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point \(S_0 \) of the system, and if \(S_0 \) is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this and similar systems were obtained earlier.

中文翻译：

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基因网络模型中的不变表面

摘要

我们在某个六维动力系统的相图中构造了不变的二维表面，该系统被视为圆形基因网络功能的模型。该不变曲面包含系统的平衡点\（S_0 \），如果\（S_0 \）是双曲的，则此曲面包含系统的一个循环。此系统和类似系统存在一个循环的条件是较早获得的。