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Exploring the collective behavior of interacting entities is of greatinterest and importance. Rather than focusing on static and uniformconnections, we examine the co-evolution of diverse mobile agents experiencingvarying interactions across both space and time. Analogous to the socialdynamics of intrinsically diverse individuals who navigate between and interactwithin various physical or digital locations, agents in our model traverse acomplex network of heterogeneous environments and engage with everyone theyencounter. The precise nature of agents internal dynamics and the variousinteractions that nodes induce are left unspecified and can be tailored to suitthe requirements of individual applications. We derive effective dynamicalequations for agent states which are instrumental in investigating thresholdsof consensus, devising effective attack strategies to hinder coherence, anddesigning optimal network structures with inherent node variations in mind. Wedemonstrate that agent cohesion can be promoted by increasing agent density,introducing network heterogeneity, and intelligently designing the networkstructure, aligning node degrees with the corresponding interaction strengthsthey facilitate. Our findings are applied to two distinct scenarios: thesynchronization of brain activities between interacting individuals, asobserved in recent collective MRI scans, and the emergence of consensus in acusp catastrophe model of opinion dynamics.

Consensus Formation Among Mobile Agents in Networks of Heterogeneous Interaction Venues