Modeling and analyzing large swarms with covert leaders

Sun, Yu
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University of Delaware
Swarm dynamics is the study of collections of agents that interact with one another without central control. We would like to build a model to simulate the behavior of swarms with covert leaders. Then based on the model, we would like to know the stability of the system, the collective decision of the swarms when there is knowledge confliction, and the way to find the covert leaders when we observe a group of individuals in motion. In Chapter 1, we extend the covert leadership model in large swarms. A leader is a member of the swarm that acts upon information in addition to what is provided by local interactions. A covert leader is a leader that is treated no differently than others in the swarm, so leaders and followers participate equally in whatever interaction model is used. We focus our efforts on the behaviors driven by the three-zone swarming model and present a new nonlinear model in which leaders will respond more strongly to additional information when the swarm is less dense. Similarly, leaders in dense regions behave more like followers. In Chapter 2, we perform linear stability analysis on the model. The result is the same as the leaderless model, which says that the growth or decay of perturbations in an infinite, uniform swarm depends on the strength of attraction relative to repulsion and orientation. It tells us that we could inject additional information into the system without changing the stability criteria. We verify our analysis with simulation. We also compare our model with more popular linear leadership models. The leaders in our model are embedded in the swarms instead of accumulating into the front in contrast to the linear model. We apply this model to wireless robotic applications, in which densities are calculated utilizing positions of neighboring robots. The result on the QualNet platform is consistent with our ideal simulation results. In Chapter 3, we explore problems where two classes of covert leaders with different information try to influence the same swarm. The swarms will choose the average direction if the information differential is small. The swarms will randomly choose a direction of the leaders' if the information differential is large. We validate our modeling and analysis using realistic wireless protocols and channel models on the QualNet network simulator. We also perform two case studies which are simplified forms of our model to find the bifurcation point analytically. In Chapter 4, we try to solve the problem: whether or not it is possible to distinguish between followers and leaders when we observe a group of individuals in motion. We explore the interplay between swarm dynamics, covert leadership and theoretical information transfer. Depending upon the leadership model, leaders can use their external information either all the time or in response to local conditions. We use theoretical information transfer as a means of analyzing swarm interactions. We find that covert leaders can be distinguished from followers in a swarm because they receive less transfer entropy than followers. Finally, in Chapter 5, we would like to find a method to detect who are the leaders and who are the followers. Inspired by the PageRank method which is used by Google to rank the importance of web pages, we apply a modified PageRank method to the swarms. We test this method on the Couzin model so that we could control the weight of the external information that the leaders respond to. We find that the method works well when the leaders respond to the external information relatively strongly which means the weight of the external information that the leaders respond to should be above O (10-2 ). To our nonlinear model, the weight is changing with time and below O (10-2 ). This method can not detect the leaders in our model. From this point of view, the leaders in our model really are covert. (Abstract shortened by UMI.)