This paper 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. Further, 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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受非相同拓扑约束的有向符号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签名网络的收敛行为。此外，代理受制于由具有强连接联合的两个不同有符号有向图表示的不相同拓扑。结果表明，当考虑受符号一致的非相同拓扑约束的有符号网络时，当且仅当两个有符号有向图的并集在结构上是平衡的（分别为不平衡的）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，签名网络总是可以保证被中和。