论文标题
耦合网络中组织节奏活动的全球分叉
A global bifurcation organizing rhythmic activity in a coupled network
论文作者
论文摘要
我们研究了一个不变圆分叉上的鞍节点附近的耦合相振荡器系统，并由随机固有频率驱动。在控制参数的变化下，系统经历了相变，改变了集体动力学的定性属性。使用Ott-Antonsen的还原和几何技术来用于普通微分方程，我们在圆柱体上的矢量场中确定了杂斜方分叉，这解释了集体动力学的变化。具体而言，我们表明，杂斜分叉将两个拓扑不同的极限周期的家族分开：分叉后非合同的分叉循环。这两个家庭对于手头模型都稳定。
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the qualitative properties of collective dynamics. Using the Ott-Antonsen reduction and geometric techniques for ordinary differential equations, we identify a heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that the heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before the bifurcation from noncontractibile ones after the bifurcation. Both families are stable for the model at hand.
