Emergence Of Bicluster Aggregation For The Swarm Sphere Model With Attractive-repulsive Couplings
July 17, 2020 - Ha, Seung-Yeal; Kim, Dohyun; Lee, Jaeseung; Noh, Se Eun
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EmailJournal or Book Title: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Volume/Issue: 19
Year Published: 2020
We study emergent behaviors of the swarm sphere model under attractive-repulsive couplings and present several sufficient frameworks leading to the complete and practical bicluster aggregations using two key ingredients (two-point correlation function and order parameter). From the modeling perspective, we consider a composite ensemble consisting of two subensembles, and the intracoupling strength in the same group is positive (attractive); in contrast, the inter coupling strength between different groups is negative (repulsive). For the modeling of frequency matrices, we classify them into four classes (fully identical, weakly identical, weakly nonidentical, and fully nonidentical) and present sufficient frameworks leading to emergent bicluster aggregations. More precisely, for the fully identical cases, we show that the complete bipolar aggregation emerges from some well-prepared initial data. For the weakly identical case, we show that the relative distances in the same group converge to zero; however, they are not well separated so that the complete bipolar aggregation fails. On the other hand, we prove that the practical bipolar aggregation occurs by letting the intercoupling strength tend to infinity. We also impose a specific structure on the frequency matrices to guarantee the complete bipolar aggregation for the weakly nonidentical case. Finally, we present several numerical examples to illustrate the robustness of our theoretical results.
DOI: 10.1137/19M1265922
Type of Publication: Article
