论文标题
免费振荡器网络中的爆炸性行为
Explosive behaviour in networks of Winfree oscillators
论文作者
论文摘要
我们考虑使用挥发器的定向网络，具有电源法分布在内部和超级分布的网络。高斯和幂定律分布了固有频率，并且这些频率与振荡器的数度正相关。 OTT/ANTONTEN ANSATZ用于为网络的预期动力学得出基于度的平均场方程，并通过数值分析这些方程。在各种情况下，发现两个不同的稳态或稳态和周期性解决方案之间的“爆炸性”过渡，并使用分叉理论来解释这些转变。
We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are considered, and these frequencies are positively correlated with oscillators' in-degrees. The Ott/Antonsen ansatz is used to derive degree-based mean field equations for the expected dynamics of networks, and these are numerically analysed. In a variety of cases "explosive" transitions between either two different steady states or between a steady state and a periodic solution are found, and these transitions are explained using bifurcation theory.
