arXiv subjects

Haoyang Qian

Publications and source records attributed to Haoyang Qian.

3 recordsLinked to original sources

arXiv2026

Complexity Reveals the Microscopic Origins of Macroscopic Dynamics

Real complex systems often exhibit collective transitions emerging from interactions across many components. Classical stability theory describes such transitions in spectral space, where dynamics is organized by spatially extended global eigenmodes whose collective nature obscures direct association with individual physical components. Here, we show that structural disorder in empirical random networks can fundamentally alter this picture. These properties induce spectral localization, causing Laplacian modes to concentrate on small subsets of nodes and producing a mode--node correspondence in which collective dynamics becomes governed predominantly by the local behavior of a dominant node together with their effective coupling to the surrounding network. As a consequence, stability properties can be interpreted directly in node space rather than purely in spectral space. Exploiting this principle, we develop a node-resolved framework that predicts transition onsets, identifies the nodes responsible for emergent collective behavior, and restores interpretability in systems where classical modal theories fail. In heterogeneous reaction networks, the same mechanism gives rise to exotic collective states where different subsets of nodes develop distinct dynamical behaviors beyond those associated with homogeneous assumptions. Our results show that complex network structures naturally generate spectral localization, revealing the microscopic drivers of macroscopic dynamics.

nlin.PS↗

arXiv2025

Mesoscale community organization governs epidemic onset and spread in metapopulations

Understanding how internal community structure shapes the course of epidemics remains a fundamental challenge in modeling real-world populations. Standard metapopulation models often assume uniform mixing within communities, overlooking how internal heterogeneity affects global outcomes. Here, we develop a general framework for epidemic spreading in hierarchically structured metapopulations, where individuals interact locally within dense communities and move across a broader network. We show that transmission dynamics are governed by the mesoscale organization of these communities: highly connected groups accelerate and amplify outbreaks, while less connected ones dampen spread. Through a combination of mean-field theory, spectral analysis, and stability methods, we reveal a direct link between internal connectivity and the emergence of uneven, spatially structured epidemic patterns. We further validate these predictions using real-world data, where social contact networks capture the local scale of transmission while spatial transport networks govern global connectivity, confirming the robustness of our framework across scales. These results demonstrate how community structure fundamentally governs the shape of epidemics in complex, networked populations, offering new insights into vulnerability, containment, and epidemic control.

physics.soc-ph↗

arXiv2025

Explosive opinion spreading with polarization and depolarization via asymmetric perception

Polarization significantly influences societal divisions across economic, political, religious, and ideological lines. Understanding these mechanisms is key to devising strategies to mitigate such divisions and promote depolarization. Our study examines how asymmetric opinion perception, modeled through nonlinear incidence terms, affects polarization and depolarization within structured communities. We demonstrate that such asymmetry leads to explosive polarization and causes a hysteresis effect responsible for abrupt depolarization. We develop a mean-field approximation to explain how nonlinear incidence results in first-order phase transitions and the nature of bifurcations. This approach also helps in understanding how opinions polarize according to underlying social network communities and how these phenomena intertwine with the nature of such transitions. Numerical simulations corroborate the analytical findings.

physics.soc-ph↗