2025/01/01 by Junhyeok Byeon, Seung‐Yeal Ha, Myeongju Kang +1
Computer Science · Physics and Astronomy · Mathematics · #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Mathematical Biology Tumor Growth
paper · doi:10.1111/sapm.70006
ABSTRACT We study the predictability of asymptotic clustering patterns in a first‐order nonlinear consensus model on receiver network on the real line. Nonlinear couplings between particles (agents) are characterized by an odd, locally Lipschitz, and increasing function. The proposed consensus model and its clustering dynamics is motivated by the one‐dimensional Cucker–Smale flocking model. Despite the complexity registered by heterogeneous couplings, we provide a sufficient framework to predict asymptotic dynamics such as particles' aggregation, segregation, and clustering patterns. We also verify the robustness of clustering patterns to structural changes such as relativistic effects implemented by the suitable composition of functions.