This article addresses the behavior analysis problems for directed signed networks that involve cooperative-antagonistic interactions among agents. Of particular interest is to explore the convergence behaviors of directed signed networks with agents of mixed first-order and second-order dynamics. Furthermore, the agents are subject to nonidentical topologies represented by two different signed digraphs that have a strongly connected union. It is shown that when considering signed networks subject to sign-consistent nonidentical topologies, polarization (respectively, neutralization) can be achieved if and only if the union of two signed digraphs is structurally balanced (respectively, unbalanced). By comparison, signed networks can always be guaranteed to become neutralized in the presence of sign-inconsistent nonidentical topologies.

中文翻译：

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非全同拓扑有向有向网络的收敛行为分析


本文解决了涉及代理之间合作-对抗交互的有向签名网络的行为分析问题。特别感兴趣的是探索具有混合一阶和二阶动力学代理的有向符号网络的收敛行为。此外，代理受到由两个具有强连接并集的不同符号有向图表示的不同拓扑的影响。结果表明，当考虑符号一致的非相同拓扑的符号网络时，当且仅当两个符号有向图的并集在结构上平衡（分别为不平衡）时，才能实现极化（分别为中和）。相比之下，在存在符​​号不一致的不相同拓扑的情况下，符号网络始终可以保证被中和。