Opinion Dynamics with Heterogeneous Belief Systems and State-Dependent Susceptibility on Signed Social Networks.

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Bibliographic Details
Title:	Opinion Dynamics with Heterogeneous Belief Systems and State-Dependent Susceptibility on Signed Social Networks.
Authors:	Yu, Shun¹ yushun0303@163.com, Song, Haoran² shr15005544022@163.com, Mei, Chunhui³ mch413@163.com, He, Guang⁴ hg-1211ok@163.com
Source:	IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2035-2043. 9p.
Subjects:	Consensus (Social sciences), Nonlinear systems, Stability theory, Polarization (Social sciences), Collective behavior
Abstract:	This paper introduces a generalized nonlinear model for opinion dynamics on signed social networks, which incorporates state-dependent susceptibility functions and multi-dimensional opinion spaces. Going beyond conventional scalar-state frameworks, the proposed model integrates agent-specific internal coupling matrices to capture the complex interdependencies among different opinion dimensions within individuals. By synthesizing tools from graph theory, nonlinear systems analysis, and LaSalle's invariance principle, we establish a comprehensive framework for convergence analysis, applicable to both structurally balanced and unbalanced networks. For structurally balanced networks, we demonstrate that bipartite consensus emerges. In contrast, structurally unbalanced configurations lead to distinct convergence behaviors, characterized by the nullspace properties of the system matrix. Our results provide rigorous sufficient conditions for exponential convergence across diverse behavioral archetypes including stubborn positives, neutrals, and extremists and reveal how network topology, susceptibility profiles, and interaction types collectively govern the system dynamics. This work establishes a unified theoretical foundation for studying multi-consensus dynamics in complex networked systems, with implications for understanding polarization and the emergence of collective behavior in systems with cooperative-antagonistic interactions. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This paper introduces a generalized nonlinear model for opinion dynamics on signed social networks, which incorporates state-dependent susceptibility functions and multi-dimensional opinion spaces. Going beyond conventional scalar-state frameworks, the proposed model integrates agent-specific internal coupling matrices to capture the complex interdependencies among different opinion dimensions within individuals. By synthesizing tools from graph theory, nonlinear systems analysis, and LaSalle's invariance principle, we establish a comprehensive framework for convergence analysis, applicable to both structurally balanced and unbalanced networks. For structurally balanced networks, we demonstrate that bipartite consensus emerges. In contrast, structurally unbalanced configurations lead to distinct convergence behaviors, characterized by the nullspace properties of the system matrix. Our results provide rigorous sufficient conditions for exponential convergence across diverse behavioral archetypes including stubborn positives, neutrals, and extremists and reveal how network topology, susceptibility profiles, and interaction types collectively govern the system dynamics. This work establishes a unified theoretical foundation for studying multi-consensus dynamics in complex networked systems, with implications for understanding polarization and the emergence of collective behavior in systems with cooperative-antagonistic interactions. [ABSTRACT FROM AUTHOR]
ISSN:	19929978