# Convergence Behavior Analysis of Directed Signed Networks Subject to Nonidentical Topologies

## TL;DR

This paper analyzes the convergence behaviors of directed signed networks with mixed agent dynamics and nonidentical topologies, revealing conditions for polarization, neutralization, and the impact of topology consistency.

## Contribution

It provides a comprehensive analysis of how nonidentical signed digraph topologies influence convergence, polarization, and neutralization in directed signed networks with mixed agent dynamics.

## Key findings

- Polarization occurs if and only if the union of topologies is structurally balanced.
- Neutralization can always be achieved with sign-inconsistent topologies.
- Sign-consistent topologies lead to polarization or neutralization depending on structural balance.

## Abstract

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.