Abstract We investigate the dynamical robustness property of the damaged network of active and inactive oscillators under the influence of the mean-field diffusion. The tolerance of dynamical activity of the entire coupled network has realized through the aging transition in the coupled dynamical network. We analytically derived the critical threshold of mean-field density and coupling values for the appearance of the aging transition in the damaged network. By using the critical values as a quantifiable measure of dynamical robustness of the damaged network, we showed that higher mean-field value is favorable to increase the dynamical robustness of the entire network. We also perform the numerical experiment on the network of Stuart-Landau oscillators and the obtained numerical results have an excellent agreement with the analytical findings. Finally, we extend our investigation into the coupled time-delayed network and discussed the affirmative influence of the mean-field parameter on the dynamical robustness of the network.

中文翻译：

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平均场对受损网络老化转变的影响

摘要 我们研究了受平均场扩散影响的有源和无源振荡器损坏网络的​​动态鲁棒性。整个耦合网络的动态活动容忍度是通过耦合动态网络中的老化过渡实现的。我们通过分析推导出了平均场密度的临界阈值和损坏网络中出现老化转变的耦合值。通过使用临界值作为受损网络动态鲁棒性的可量化度量，我们表明较高的平均场值有利于提高整个网络的动态鲁棒性。我们还在 Stuart-Landau 振荡器网络上进行了数值实验，所得数值结果与分析结果非常吻合。