论文标题
随机步进扩散的振荡器网络中的振幅死亡和恢复
Amplitude death and restoration in networks of oscillators with random-walk diffusion
论文作者
论文摘要
我们研究了通过随机游动扩散结合的振荡器网络中集体振荡的死亡和恢复。与用于建模化学反应的常规扩散耦合不同，这里的未耦合单元的平衡不是耦合集合的解决方案。取而代之的是，连接性修改了原始的不稳定固定点和稳定的极限周期，使它们依赖于节点。使用随机网络中的数值模拟，我们表明，在某些情况下，这种扩散引起的异质性通过HOPF分叉稳定了最初不稳定的固定点。进一步提高耦合强度也可以恢复振荡。通过对稳定性特性的数值分析，我们得出结论，这是振幅死亡的新病例。最后，我们使用系统的异质平均场减少，以证明这种现象在增加系统大小时的稳健性。
We study the death and restoration of collective oscillations in networks of oscillators coupled through random-walk diffusion. Differently than the usual diffusion coupling used to model chemical reactions, here the equilibria of the uncoupled unit is not a solution of the coupled ensemble. Instead, the connectivity modifies both, the original unstable fixed point and the stable limit-cycle, making them node-dependent. Using numerical simulations in random networks we show that, in some cases, this diffusion induced heterogeneity stabilizes the initially unstable fixed point via a Hopf bifurcation. Further increasing the coupling strength the oscillations can be restored as well. Upon numerical analysis of the stability properties we conclude that this is a novel case of amplitude death. Finally we use a heterogeneous mean-field reduction of the system in order to proof the robustness of this phenomena upon increasing the system size.
