五节律电路的定性和定量稳定性分析
Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits
摘要：
弛张振荡器的抑制回路是生物网络动力学的常用模型。我们提出了一个定性和定量的稳定性分析这样的电路构成的三个耦合振荡器的Fitzhugh-Nagumo型节点。取决于抑制强度和单个振荡器的参数，该电路表现出多达五个同时稳定的节奏的多节律性。与方法的分歧分析和相位减少，我们调查定性变化的稳定性，这些电路的节奏在很宽的参数范围。此外，我们量化如何鲁棒的节奏下保持随机扰动监测电路中的相位扩散。我们的研究结果使我们能够描述电路动态与单个节点的动态。我们还发现，定量和定性的多节律性的稳定性并不总是一致的。
英文摘要：
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled oscillators of a Fitzhugh-Nagumo type as nodes. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmicity of up to five simultaneously stable rhythms. With methods of bifurcation analysis and phase reduction, we investigate qualitative changes in stability of these circuit rhythms for a wide range of parameters. Furthermore, we quantify how robustly rhythms are maintained under random perturbations by monitoring phase diffusion in the circuit. Our findings allow us to describe how circuit dynamics relate to dynamics of individual nodes. We also find that quantitative and qualitative stability of polyrhythmicity do not always align.
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