论文标题
在三个法定感应耦合的相同环振荡器中，异常不均匀的极限循环的出现和演变
Emergence and evolution of unusual inhomogeneous limit cycles displacing hyperchaos in three quorum-sensing coupled identical ring oscillators
论文作者
论文摘要
我们证明，在三个相同的环振荡器（3基因网络称为抑制剂）的系统中可以观察到强烈的不对称极限循环，该系统通过信号分子扩散以类似于已知的细菌“ Quorum-Senspement”机制的方式添加到模型中。这些周期在耦合强度的宽间隔内稳定，在很大一部分参数中，它们驱除了三个阻遏物中存在的主要高旋转状态。一个不均匀极限周期的分叉，一个振荡器的高振幅轨道和两个低振幅相同的轨道是其他两个轨道的追踪。分叉分析揭示了一系列异常的分叉级联反应以新的极限周期出现，并以拆分（略有非相同）的低振幅轨道旋转。这两个周期在小参数间隔内都失去了稳定性的无约束性混乱。 HyperChaos在“岛”周围的参数平面中占主导地位，并具有无孔的极限循环，当系统扰动后系统恢复到稳定的不对称周期时，这说明了很长的高混沌瞬变。反过来，循环在高旋转轨迹中造成了不对称且通常很长的碎片。所提出的周期与已知的不对称吸引子不同：由“振荡死亡”和“最小嵌合体”观察到的循环所生的不均匀极限周期。
We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like the known bacterial "quorum-sensing" mechanism. These cycles are stable over a wide interval of the coupling strengths where they expel the dominant hyperchaotic regime existing in three Repressilators in very large areas of parameters. The bifurcations of the inhomogeneous limit cycle, with a high-amplitude orbit for one oscillator and two low-amplitude identical orbits for the other two, are traced. Bifurcation analysis reveals an unusual cascade of bifurcations ended in the appearance of a new limit cycle with splitted (slightly nonidentical) low-amplitude orbits. Both cycles lose stability giving birth inhomogeneous chaos in the small parameter interval. Hyperchaos dominates in the parameter plane around the "island" with inhomogenous limit cycles, and this accounts for very long hyper chaotic transients when the system is returning to stable asymmetric cycles after their perturbations. In turn, it is the cycles that contribute the asymmetric and often rather long pieces in hyperchaotic trajectories. The presented cycles differ from the known asymmetric attractors: inhomogeneous limit cycles born from "oscillating death" and the cycles observing in "smallest chimeras".
