We investigate a multi-agent model of firms in a Research & Development (R&D) network. Each firm is characterized by its knowledge stock x_i(t), which follows a non-linear dynamics. x_i(t) grows with the input from other firms, i.e., by knowledge transfer, and decays otherwise. However, maintaining the interactions that increase knowledge stock is costly for all partners involved. Because of this, firms leave the network whenever their expected knowledge growth is not realized. This, in turn, may cause other firms also to leave the network. The paper discusses two bottom-up intervention scenarios to prevent, reduce, or delay such cascades of firms leaving. The first one is based on the formalism of network controllability, in which driver nodes are identified and subsequently incentivized, by reducing their costs. The second one combines node interventions and network interventions. It proposes the controlled removal of a single firm and the random replacement of firms leaving. This allows to generate small cascades, which prevents the occurrence of large cascades. We find that both approaches successfully mitigate cascades and thus improve the resilience of the R&D network.

我们研究了研究与开发（R＆D）网络中公司的多主体模型。每家公司都有自己的知识储备X_一世（Ť），它遵循非线性动力学。 X_一世（Ť）随着其他公司的投入（即知识转移）而增长，反之则衰落。但是，保持互动以增加知识储备对于所有相关合作伙伴来说都是昂贵的。因此，只要未实现预期的知识增长，企业就会离开网络。反过来，这可能导致其他公司也离开网络。本文讨论了两种自下而上的干预方案，以防止，减少或延迟这种级联的企业退出。第一个基于网络可控制性的形式主义，其中通过减少驱动程序节点的成本来确定驱动节点并随后对其进行激励。第二个结合了节点干预和网络干预。它提出了对单个企业的有控制的撤离和对企业离开的随机替代的建议。这样可以生成小的级联，这样可以防止大瀑布的发生。我们发现，这两种方法都能成功缓解级联，从而提高R＆D网络的弹性。