Research on Group Behavior Modeling and Individual Interaction Modes with Informed Leaders

Yude Fu, Jing Zhu, Xiang Li, Xu Han, Wenhui Tan, Qizi Huangpeng () and Xiaojun Duan
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Yude Fu: College of Science, National University of Defense Technology, Changsha 410073, China
Jing Zhu: College of Economic and Management, Beijing Jiaotong University, Beijing 100044, China
Xiang Li: College of Science, National University of Defense Technology, Changsha 410073, China
Xu Han: College of Science, National University of Defense Technology, Changsha 410073, China
Wenhui Tan: College of Science, National University of Defense Technology, Changsha 410073, China
Qizi Huangpeng: College of Science, National University of Defense Technology, Changsha 410073, China
Xiaojun Duan: College of Science, National University of Defense Technology, Changsha 410073, China

Mathematics, 2024, vol. 12, issue 8, 1-23

Abstract: This study investigates coordinated behaviors and the underlying collective intelligence in biological groups, particularly those led by informed leaders. By establishing new convergence condition based on experiments involving real biological groups, this research introduces the concept of a volitional term and heterogeneous networks, constructing a coupled-force Cucker–Smale model with informed leaders. Incorporating informed leaders into the leader-follower group model enables a more accurate representation of biological group behaviors. The paper then extracts the Flock Leadership Hierarchy Network (FLH), a model reflecting real biological interactions. Employing time slicing and rolling time windows, the study methodically analyzes group behavior stages, using volatility and convergence time as metrics to examine the relationship between group consistency and interactions. Comparative experiments show the FLH network’s superior performance. The Kolmogorov-Smirnov test demonstrates that the FLH network conforms to a power-law distribution, a prevalent law in nature. This result further illuminates the crucial role that power-law distribution plays in the evolutionary processes of biological communities. This study offers new perspectives on the evolution of biological groups, contributing to our understanding of the behaviors of both natural and artificial systems, such as animal migration and autonomous drone operations.

Keywords: coordinated behavior; informed leaders; group consistency; biological interaction; power-law distribution; complex network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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