Juan Velez-Rojas, M. G. Cosenza

Griffiths phases provide a mechanism for sustaining critical dynamics over extended parameter regions without fine-tuning to an isolated transition point. This behavior has been mainly associated with structural heterogeneity in complex networks. Here we show that quenched heterogeneity in local parameters can generate a chaotic Griffiths phase in a network of map-based neurons. We study globally coupled Chialvo maps with quenched disorder in a local neuronal parameter, thereby isolating intrinsic parameter disorder from topological disorder. As the coupling strength is varied, a chaotic Griffiths phase emerges between desynchronized and coherent chaotic dynamics, characterized by intermittent formation and breakup of neuronal clusters and large fluctuations in the fraction of clustered neurons. Within this regime, cluster sizes exhibit power-law distributions with coupling-dependent exponents, providing evidence of critical behavior over a finite parameter interval. The chaotic Griffiths phase is absent in the homogeneous limit and broadens progressively as the degree of parameter heterogeneity increases. We further introduce topological disorder through small-world connectivity and find that its combined action with local parameter heterogeneity substantially extends the chaotic Griffiths phase. In both globally coupled and small-world networks, the number of positive Lyapunov exponents displays anomalous scaling with system size. These results demonstrate that intrinsic dynamical heterogeneity constitutes an independent mechanism for generating chaotic Griffiths phases and that its interplay with structural disorder enhances extended criticality in neuronal networks.

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Kevin Paramero-Arias, Alejandro P. Riascos

We study synchronization in network-coupled oscillators subject to stochastic resetting of a subset of nodes. We show that resetting can induce collective coherence in oscillators that are never directly reset, through the interplay of network structure, frequency heterogeneity, and the organization of the reset subsystem. In the infinite-resetting-rate limit, the reset nodes become effectively pinned to a reference phase, and linearization near synchronization maps the dynamics of the remaining subsystem onto a grounded-Laplacian problem. This formulation yields an analytical relation between the synchronization level and the reset parameters, providing an estimate of the coupling strength required to achieve a prescribed degree of coherence. Beyond the linear regime, we develop a mean-field description in which the reset subsystem acts as an effective ordering field for the remaining oscillators. Numerical simulations across different network topologies confirm these predictions and show that synchronization is enhanced by increasing both the reset fraction and network connectivity. In heterogeneous networks, the placement of reset nodes can strongly influence the synchronization response. For frequency distributions with nonzero mean, resetting competes with the intrinsic collective rotation and can drive the system from a rotating synchronized state to a phase-locked state. These results establish subsystem resetting as a mechanism for inducing and controlling collective synchronization in complex networks.

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A.N. Montanari, P. Zanin, A.E. Motter,  
Science 393, 6817 (2026). 

Previous studies of network dynamics have suggested that heterogeneity among nodes inhibits stability, which is at odds with the ubiquity of inherently heterogeneous natural and engineered systems. Here, we show that this conclusion arises from model reductions introduced for mathematical tractability and breaks down when nodal dynamics are higher-dimensional, yielding non-Hermitian Jacobians. In such systems, including neural, power-grid, and material networks, nodal heterogeneity can instead enhance stability, even when parameters are randomly disordered. Non-Hermiticity also underlies the stabilizing effects of network heterogeneity, which can arise even in one-dimensional nodal dynamics through nonreciprocal interactions, as shown for ecological networks. Our framework reveals disorder not as a liability but as a general resource for stabilizing complex systems.

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János Kertész, Marc Barthelemy, Guido Caldarelli, Bikas K. Chakrabarti, Tiziana Di Matteo, Serge Galam, Marta Gonzales, Yurij Holovatch, Janusz A. Holyst, Sarika Jalan, Hawoong Jeong, Neil F. Johnson, Renaud Lambiotte, Linyuan Lü, Thomas Lux, Rosario N. Mantegna, Matjaz Perc, Jari Saramäki, Michael Small, Misako Takayasu, Taha Yasseri, Wei-Xing Zhou

Social Physics seeks quantitative, empirically testable explanations of collective human behavior. Its name has a long and contested history, but its contemporary program is neither the claim that society is literally a physical system nor an attempt to replace the social sciences with physics. It is an interdisciplinary practice: observation and experimentation, model construction, mathematical and computational analysis, and repeated confrontation with data. The field has been transformed by analyzing digital traces, network science, agent-based modeling, large-scale experiments, and the capacity to study coupled dynamics across economic, social, technological, biological, and physical layers. We review advances in financial analysis and modeling; economic complexity; the structure and evolution of social networks; spreading, opinion, and information dynamics; inequality, cooperation, conflict, mobility, cities, culture, science, and collective behavior; and the emerging study of human-AI ecosystems. Across these domains, common features recur – heterogeneity, interaction, feedback, adaptation, non-equilibrium dynamics, multiscale organization, and emergent collective outcomes. We also confront the limitations that have arisen in this field: convenience samples, platform dependence, weak causal identification, over-universal claims, insufficient engagement with meaning and institutions, privacy risks, and the danger that predictive models become instruments of manipulation. We propose a future Social Physics organized around theory – data reciprocity; causal and generative explanation; measurement validity and cross-context generalization; responsible, participatory data governance; genuinely interdisciplinary collaboration; and reflexive study of interventions and algorithms that alter the systems being observed.

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Rapid advances in large language models (LLMs) have empowered autonomous agents to generate social networks, communicate, and form shared and diverging opinions on political issues. However, our understanding of their collective behaviours and underlying mechanisms remains incomplete. In this paper, we simulate networked systems involving thousands of LLM agents across different backbone models (GPT-3.5, GPT-4o, ChatGLM, Llama-3, and DeepSeek-V3), in which agents interact through LLM-guided conversations and update their opinions over time, resulting in the emergence of opinion polarization. We discover that these agents spontaneously develop their own social network with properties characteristic of human social networks, such as homophilic clustering. The collective opinions of these LLM agents evolve in ways that exhibit behavioural patterns consistent with social phenomena and mechanisms widely discussed in empirical studies of human behaviour and opinion-dynamics models. This consistency suggests that LLM agents can serve as a valuable synthetic testbed for exploring hypothetical intervention strategies in networked LLM-agent systems. Using this testbed, we further examine the effects of a range of network- and individual-level interventions, such as promoting more diverse interactions and reducing confirmation bias. Overall, this work not only sheds light on subtle opinion dynamics and collective behaviour of LLM agents from a network perspective, but also demonstrates their potential for testing hypotheses about opinion dynamics and intervention strategies.

Jinghua Piao, Zhihong Lu, Chen Gao, Fengli Xu, Qinghua Hu, Fernando P. Santos, Yong Li & James Evans 

Nature Communications (2026)

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