The recently introduced complex active optical network (LANER) generalizes the concept of laser system to a collection of links, building a bridge with random-laser physics and quantum-graphs theory. So far, LANERs have been studied with a linear approach. Here, we develop a nonlinear formalism in the perspective of describing realistic experimental devices. The propagation along active links is treated via suitable rate equations, which require the inclusion of an auxiliary variable: the population inversion. Altogether, the resulting mathematical model can be viewed as an abstract network, its nodes corresponding to the fields along the physical links. The dynamical equations differ from standard network models in that, they are a mixture of differential delay (for the active links) and algebraic equations (for the passive links). The stationary states of a generic setup with a single active medium are thoroughly discussed, showing that the role of the passive components can be combined into a single transfer function that takes into account the corresponding resonances.

最近推出的复杂有源光网络（LANER）将激光系统的概念概括为一系列链接，并建立了具有随机激光物理学和量子图理论的桥梁。到目前为止，已经使用线性方法研究了LANER。在这里，我们从描述现实实验设备的角度发展了非线性形式主义。沿活动链路的传播通过适当的速率方程进行处理，这需要包括一个辅助变量：总体反演。总而言之，可以将所得的数学模型视为一个抽象网络，其节点对应于沿物理链接的字段。动态方程与标准网络模型的不同之处在于，它们是差分延迟（对于主动链路）和代数方程（对于被动链路）的混合。