From Group Formation To Group Fission:Modeling And Analysis Of The Self-organized Collective Motion Of Flocks

Collective motion is a common phenomenon which is deeply rooted in nature and occurs at all levels of living organisms. Some of the striking examples such as schools of fish, flocks of birds, swarm of locusts, bacterial colonies, swarming microtubules and human crowd are covered. The coordinated and ordered collective motion of such groups that consist of a large amount of individuals is thought to emerge from a rela-tively simple and local self-organizing interaction between near-neighbors. Revealing and understanding the connection between the traits at the level of individual and of the group are regarded as the essential objective of the theoretical researches and the empirical studies in this field. The related findings could not only provide insight into the underlying mechanism of animal-flocks, but also provide prototype for the design, construction and optimization of the distinctive man-made swarm systems such as swarm robotics, particles swarm algorithm and etc. Thus, apart from the theoretical interest, the research of swarm also demonstrates its universal application.In this thesis, on the basis of analyzing the behavior of animal-flocks, the collec-tive motion is categorized into two types, the group formation and the group fission; then, we extend the research topics merely on the process of group formation to a new perspective which focuses on the group fission behavior. In order to describe the mo-tion features of the flocks, some novel individual-based flocking models which have the capacities to reproduce the behavior of group formation and group fission are devel-oped according to the features such as intermittent pairwise interaction and selective attention among animals. The main contributions of this thesis are as following:Firstly, a social-force based modeling framework is developed according to the behavioral rules of "Segregation-Alignment-Cohesion" after summarizing the behav-ioral characters of animals from the recent empirical literatures. In the framework, we emphasize that the key aspect of reproducing the fission behavior of flocks is to model the Alignment behavior with an evidence-driven manner instead of the classical assumption of "average-velocity". Meanwhile, we explore the collective response pat-terns of flocks under external stimulus; and some order parameters and performance indexes are introduced and defined to characterize the behavior of group formation and group fission quantitatively.Secondly, on the basis of utilizing the traditional SAC-Ave flocking model with "averaged" coordination strategy between n-nearest neighbors, we investigate the func-tional limitations of classical assumption of "average-velocity" from the perspective of group fission. By exploring the collective response of SAC-Ave under external stim-ulus, we find that it endows the property of group cohesion and velocity consensus on the ensemble, which could be essential for reproducing the process of group for-mation. But it will prevent a coherent flock from splitting into multiple sub-groups under external conflicting stimulus. In addition, the strategy of averaging the states of n-nearest neighbors will dampen out any novel signal or cue like the abrupt escape maneuver. This dilution effect inhibits the efficiency of response to the local stimulus, which is distinct from the rapid directional shifts across the ensemble triggered by a single startled individual of animal flocks.Thirdly, according to the behavioral features of intermittent pairwise interactions in fish schools and bird flocks, we present a novel one-neighbor-based flocking model called SAC-One, in which we suggest that the individual tends to align its motion only to one near-neighbor that shows the apparent speed variation and locates in front. In this manner we emphasize the features of sensitivity to motion change and sensory anisotropy in visual perception. Although being simpler than SAC-Ave model, this model can reproduce the behavior of group fission and group formation simultaneously; and the speed of group formation and the turning rate are all better than the perfor-mances of SAC-Ave model. Interestingly, this model predicts that the front sensory anisotropy of individuals has a nonmonotonic influence on the consensus speed and the turning rate of flocks, there exists an optimal anisotropy leading to the fastest turning and group formation. Furthermore, by employing the theory of complex dynamical network, we explain its effect of anisotropy by analyzing the topological structure of the social network formed by one-neighbor interactions in SAC-One flocks.Fourthly, an original flocking model called SAC-ICD with the feature of selec-tive attention is established according to the top-down (task-driven) attention and bottom-up (stimulus-driven) attention of visual perception. To this end, the informa-tion theory is firstly employed to define an index called information coupling degree (ICD) to formulate the computational features of visual attention. And then, an ICD-based "min-max" strategy of velocity coordination is proposed, in which the individual only needs to coordinate the speed with the most "ordered" neighbor and/or the most ’unusual" one corresponding to top-down and bottom-up attentions respectively. By investigating free-motion and stimulated-movement of SAC-ICD under different con-ditions such as stimulus free, minimal stimulus and conflicting stimulus, we show that this model can reproduce some typical self-organized behaviors including group for-mation, abrupt turning and group fission. Additionally, its performance such as the consensus speed, the response accuracy and speed are obviously better than that of the SAC-Ave and the SAC-One model. Furthermore, we find that it is very essential for the individual who remains to keep a middle level task-free attention to the novel cue of their neighbors, which would endow the flocks a more precise and quick collective response to the external stimulus.Finally, in order to verify the flocking models proposed in this thesis, a predator-prey flocking scenario is established. Then, from the perspective of reducing the risk of being captured by predator, we compare the escaping patterns of flocks and the individual living time of SAC-One and SAC-ICD with SAC-Ave model. It can be concluded that the attention-based SAC-ICD model has the ability to reproduce more typical self-organized escaping patterns as the animal flocks; and it also predicts the capability of using spare escaping cues and avoiding head-on attack effectively. The SAC-One model with selective interaction is inferior to that of SAC-ICD model, but its performance has been significantly improved compared with SAC-Ave model. In sharp contrast, the traditional average-velocity based SAC-Ave model shows a low surviving ability, and poor adaptability and flexibility to the threat of predator.