Abstract
“Chases and Escapes” is a classical mathematical problem. Recently, we proposed a simple extension, called “Group Chase and Escape,” where one group chases another. This extension bridges the traditional problem with the current interest in studying collective motion among animals, insects, and cars. In this presentation, I will introduce our fundamental model and explore its intricate emergent behaviors. In our model, each chaser approaches the nearest escapee, while each escapee moves away from its closest chaser. Interestingly, despite the absence of communication within each group, we observe the formation of aggregate patterns. Furthermore, the effectiveness of capture varies as we adjust the ratio of chasers to escapees, which can be attributed to a group effect. I will delve into how these behaviors manifest in relation to various parameters, such as densities. Moreover, we have explored different expansions of this basic model. First, we introduced fluctuations, where players now make errors in their step directions with a certain probability. We found that a moderate level of fluctuations improves the efficiency of catching. Second, we incorporated a delay in the chasers’ reactions to catch their targets. This distance-dependent reaction delay can lead to highly complex behaviors. Additionally, I will provide an overview of other groups’ extensions of the model and the latest developments in this field.
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Notes
The following website has a collection of Traveling Salesman Problems. We have used one with 52 cities, named in the list as berlin52.tsp and berlin52.opt.tour. http://elib.zib.de/pub/Packages/mptestdata/tsp/tsplib/tsp/index.html.
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Acknowledgements
The primary portion of this work was carried out in collaboration with Dr. Atsushi Kamimura from The University of Tokyo. In addition to him, the author would like to extend gratitude to the collaborators of the papers listed in the references. Thanks also goes to John G. Milton from Claremont University for the reference to literature ([3]). This work was supported by JSPS Topic-Setting Program to Advance Cutting-Edge Humanities and Social Sciences Research Grant Number JPJS00122674991.
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Toru Ohira is the presenter of this paper
This work will be presented in part as a plenary speech at the joint symposium of the 29th International Symposium on Artificial Life and Robotics, the 9th International Symposium on BioComplexity, and the 7th International Symposium on Swarm Behavior and Bio-Inspired Robotics (Beppu, Oita and Online, January 24–26, 2024).
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Ohira, T. Collective behaviors emerging from chases and escapes. Artif Life Robotics 29, 1–11 (2024). https://doi.org/10.1007/s10015-023-00928-1
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DOI: https://doi.org/10.1007/s10015-023-00928-1