Systems composed of reactive particles diffusing in a network display emergent dynamics. While Fick’s diffusion can lead to Turing patterns, other diffusion schemes might display more complex phenomena. Here we study the death and restoration of collective oscillations in networks of oscillators coupled by random-walk diffusion, which modifies both the original unstable fixed point and the stable limit-cycle, making them topology-dependent. By means of numerical simulations we show that, in some cases, the diffusion-induced heterogeneity stabilizes the initially unstable fixed point via a Hopf bifurcation. Further increasing the coupling strength can moreover restore the oscillations. A numerical stability analysis indicates that this phenomenology corresponds to a case of amplitude death, where the inhomogeneous stabilized solution arises from the interplay of random walk diffusion and heterogeneous topology. Our results are relevant in the fields of epidemic spreading or ecological dispersion, where random walk diffusion is more prevalent.

由在网络中扩散的反应性粒子组成的系统显示出动态。尽管菲克的扩散会导致图灵模式，但其他扩散方案可能会显示更复杂的现象。在这里，我们研究了由随机游走扩散耦合的振荡器网络中集体振荡的死亡和恢复，该振荡会修改原始的不稳定固定点和稳定的极限环，使其与拓扑有关。通过数值模拟，我们表明，在某些情况下，扩散引起的异质性会通过Hopf分支稳定最初不稳定的固定点。此外，进一步提高耦合强度可以恢复振荡。数值稳定性分析表明，这种现象对应于振幅死亡的情况，其中非均匀稳定解是由随机游走扩散和异构拓扑的相互作用引起的。我们的结果与流行病传播或生态分散领域有关，其中随机步行传播更为普遍。