Through the introduction of stochastic operators, the following work is an extension of previous works on robustness and resilience of compartmentalized closed-loop input-output systems. Indeed, those can be subject to the onset of external random perturbations which compromise the functioning of the input-output processing. The stochastic version of the network Price identity shows that the amplified expected dismantlement of the network structure comes from an increased expectation of external disturbers. Nevertheless, resilience can lead to a partial or full offset of threats. Furthermore, by studying the eigenvalues of the Laplacian, we provide a quantified value of connectivity to the between-subnetwork coupling. The value turns out to be greater in resilient networked structures than in the robust ones.

通过引入随机算子，接下来的工作是对以前的关于分区闭环输入输出系统的鲁棒性和弹性的工作的扩展。实际上，这些可能会受到外部随机扰动的影响，从而扰乱了输入输出处理的功能。网络价格身份的随机版本显示，网络结构的预期扩展分解来自对外部干扰因素的期望增加。但是，弹性可以导致威胁的部分或全部抵消。此外，通过研究拉普拉斯算子的特征值，我们提供了到子网间耦合的连接性的量化值。事实证明，在有弹性的网络结构中，该值大于在健壮的网络结构中。