自然界有着丰富的集群行为，从微生物、昆虫，再到鱼群鸟群，甚至哺乳动物、人类， 都在群体运动之中展现着复杂的集群行为。集群行为展现了混沌状态、自相似现象与临界 态等复杂现象，上世纪末以来是研究系统科学、复杂性科学的重要方向。在以往的研究中， 多数采用多主体模型来探究群体行为的机制。然而，这种模型只适用于描述行为稳定于某 一状态的情况，无法直接揭示自然界中的自发状态转换行为。传统模型中的同质个体机制 和仅依赖当前状态的马尔可夫决策方式，使得群体内的涨落被淹没在绝对稳定状态中，无 法充分展现群体行为的真实状态。

然而，在自然界中，真正同质化的群体是极少见的，差异性是在群体之中普遍存在的 特性。差异性所带来的的群体不稳定性以及敏感性，使得生物群体能够快速适应复杂环 境。群体之中的自组织状态转换行为，是否来源于这种差异性带来的随机性，成为了一个 值得探讨的问题。

为了研究这一问题，本文在前人用来分析鱼群运动的吸引对齐力模型上进行了修改， 并将速度差异这一在自然界普遍存在的特性引入其中。本文设计模拟计算来分析速度差异 对于传统关注的一致聚集（Schooling）行为与一致旋转（Milling）行为会造成的影响，并 分析速度差异性与这两种状态的自发转换的关系。

本文构造了速度差异程度对于群体行为的影响、速度差异比例对于群体行为的影响以 及边界作用力对于群体行为的影响三个模拟实验，发现了引入群体速度差异使群体偏向于 旋转，且在边界条件下差异群体会发生群体分裂。为了深入研究速度差异对群体状态转换 的影响，本文对实验中相同参数组下出现的状态转变现象进行了统计分析。结果显示，在 引入速度差异性的群体模型中，出现了群体领导力差异的现象。

本文主要研究内容如下：

1. 速度差异性对于群体宏观表现的影响。本文进行了速度差异程度对于群体影响的计 算模拟，发现速度差异化程度越大群体越倾向进行旋转。本文进行了速度差异比例对于群 体影响的计算模拟，发现速度差异比例越接近 50%，群体越倾向于进行旋转。速度差异程 度越大，比例越接近 50%，群体越倾向于进行旋转，而不是一致聚集。

2. 速度差异性对于群体运动状态的影响。本文对于计算模拟结果进行分析，发现速度 差异群体更容易发生状态转换，且群体发生状态转换是因为速度差异带来的群体分裂。由 于群体中速度慢的个体与速度快的个体有速度差距，在运动过程中群体会发生分裂。群体 分裂驱动群体从一个稳态中脱离，进入不稳定状态。随后，由群体中的系统对齐力机制再 次聚集群体，重新建立秩序，群体便进入了另一个状态，又回到稳定状态。群体层面的速 度差异性带来的群体不稳定性促进了群体状态转变。

3. 速度差异性群体状态转换机制分析。本文构造统计量对于差异性群体发生状态转变 前后群体的领导个体进行描述，发现群体在速度差异这种个体行为差异的情况下，会涌现 出领导力的层级结构。当群体处于稳定的状态下，群体的运动会由速度较慢的个体进行主 导，也反映了速度更慢的个体具有更强的社会性可以适应稳定群体环境；当群体处于状态 转变的不稳定状态时，群体的运动状态由高速个体而主导。自然群体中的高速个体所具有 的低社会性，可以在适应混乱的群体环境并主导群体变化，这同时也与前人研究相符合。

There are abundant collective behaviors in nature, from microorganisms, insects, to fish and birds, and even mammals and humans, all show complex collective behaviors in group movement. Since the end of the last century, collective behavior has been an important direction in the study of system science and complexity science, showing complex phenomena such as chaotic state, self- similarity phenomenon and critical state. In previous studies, the multi-agent model was used to explore the mechanism of group behavior. However, this model is only suitable for describing the situation where the behavior is stable in a certain state, and cannot directly reveal the spontaneous state transition behavior in nature. In the traditional model, the homogeneous individual mecha- nism and the Markov decision mode which only rely on the current state make the fluctuation of the group submerged in the absolute stable state, and can not fully show the real state of the group behavior.

However, in nature, truly homogeneous groups are rare, and diversity is a universal feature in groups. The population instability and sensitivity brought about by diversity enable biological groups to quickly adapt to complex environments. Whether the self-organizing state transition behavior in the group comes from the randomness brought by this difference has become a problem worth discussing.

In order to study this problem, this paper modified the model used by predecessors to analyze the attraction of fish movement, and introduced the characteristic of speed difference, which is common in nature. In this paper, a simulation is designed to analyze the effect of velocity difference on the traditional focus on Schooling and Milling behavior, and to analyze the relationship between velocity difference and the spontaneous transformation of these two states.

This paper constructs three simulation experiments on the influence of velocity difference degree on group behavior, the influence of velocity difference ratio on group behavior, and the influence of boundary force on group behavior. It is found that the introduction of group velocity difference makes the group tend to rotate, and the group splits under boundary conditions. In order 

to further study the effect of speed difference on population state transition, the state transition phenomena in the same parameter group in the experiment were statistically analyzed. The results show that in the group model with speed differences, there is a phenomenon of group leadership differences.

The main research contents of this paper are as follows:

The impact of speed differences on group macro performance. In this paper, the influence of speed difference degree on the population is simulated, and it is found that the greater the speed difference degree, the more the population tends to rotate. In this paper, the effect of velocity difference ratio on the population is simulated, and it is found that the closer the velocity differ- ence ratio is to 50%, the more the population tends to rotate. The greater the degree of velocity difference, and the closer the proportion is to 50%, the more the group tends to rotate rather than congregated.

Influence of speed difference on group motion state. By analyzing the simulation results, it is found that the state transition is more likely to occur in the population with speed difference, and the state transition occurs because of the group split caused by speed difference. Since there is a speed gap between the slow and fast individuals in the group, the group will split during move- ment. Population fragmentation drives the population out of a steady state and into an unstable state. Subsequently, by the system in the group to the unity mechanism again gathered the group, re-establish order, the group will enter another state, and return to the stable state. The group in- stability brought about by the speed difference at the group level promotes the group state change.

Analysis of group state transition mechanism of speed difference. In this paper, statistics are constructed to describe the individual leaders of different groups before and after their state changes, and it is found that the hierarchical structure of leadership will emerge in the case of individual behavior differences such as speed differences. When the group is in a stable state, the movement of the group is dominated by the slower individual, which also reflects that the slower individual has stronger sociality and can adapt to the stable group environment. When the group is in the unstable state of state change, the movement state of the group is dominated by the high- speed individual. The low sociality of high-speed individuals in natural groups can adapt to chaotic group environment and lead group changes, which is also consistent with previous studies.