We consider some piecewise linear 4-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass-Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.

中文翻译：

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分段线性动力系统的相图结构

我们考虑一些分段线性4维动力系统，该系统模拟由一个负反馈和三个正反馈调节的基因网络。Glass和Pasternack描述了该模型中存在稳定循环的条件。我们在该系统的相图中，在此稳定循环的吸引域之外，构造与Glass-Pasternack循环具有非平凡链接的不变分段线性曲面。