{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T13:23:56Z","timestamp":1791984236468,"version":"4.4.0"},"reference-count":59,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T00:00:00Z","timestamp":1698278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51709150"],"award-info":[{"award-number":["51709150"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>For a long time, fish school swimming has attracted a great deal of attention in biological systems, as fish schools can have complex hydrodynamic effects on individuals. This work adopted a non-iterative, immersed boundary\u2013lattice Boltzmann method (IB\u2013LBM). A numerical simulation of two-dimensional three-degree-of-freedom self-propelled fish, in side-by-side, staggered, and triangle formations, was conducted by adjusting spacing and motion parameters. A comprehensive analysis of individual speed gains and energy efficiencies in these formations was carried out. Furthermore, an analysis of the hydrodynamic characteristics of fish schools was performed, using instantaneous vorticity profiles and pressure fields. Certain studies have shown that passive interactions between individuals cannot always bring hydrodynamic benefits. The swimming efficiency of side-by-side formations in the same phase gradually increases as the distance decreases, but it also brings certain burdens to individuals when the phases are different. This paper also shows that the roles of passive interactions, spacing, and deflections affect fish school subsystems differently. When the low-pressure areas created by a wake vortex act on one side of an individual\u2019s body, the tail-end fish are good at gaining hydrodynamic benefits from it. This effect is not universal, and the degree to which individuals benefit from changes in exercise parameters varies. This study provides a theoretical basis for bioinspired robots, as well as providing certain insights into the mechanism of collective biological movement.<\/jats:p>","DOI":"10.3390\/biomimetics8070510","type":"journal-article","created":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T07:22:15Z","timestamp":1698304935000},"page":"510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Effects of Different Motion Parameters on the Interaction of Fish School Subsystems"],"prefix":"10.3390","volume":"8","author":[{"given":"Feihu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Guangdong Ocean University, No. 1 Haida Road, Mazhang District, Zhanjiang 524088, China"},{"name":"Shenzhen Institute of Guangdong Ocean University, No. 3 Binhai 2nd Road, Dapeng New District, Shenzhen 518120, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianhua","family":"Pang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guangdong Ocean University, No. 1 Haida Road, Mazhang District, Zhanjiang 524088, China"},{"name":"Shenzhen Institute of Guangdong Ocean University, No. 3 Binhai 2nd Road, Dapeng New District, Shenzhen 518120, China"},{"name":"Guangdong Provincial Key Laboratory of Intelligent Equipment for South China Sea Marine Ranching, Guangdong Ocean University, No. 5, Haibin Avenue Middle, Development District, Zhanjiang 524088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3030-4211","authenticated-orcid":false,"given":"Zongduo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guangdong Ocean University, No. 1 Haida Road, Mazhang District, Zhanjiang 524088, China"},{"name":"Guangdong Provincial Key Laboratory of Intelligent Equipment for South China Sea Marine Ranching, Guangdong Ocean University, No. 5, Haibin Avenue Middle, Development District, Zhanjiang 524088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junkai","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guangdong Ocean University, No. 1 Haida Road, Mazhang District, Zhanjiang 524088, China"},{"name":"Shenzhen Institute of Guangdong Ocean University, No. 3 Binhai 2nd Road, Dapeng New District, Shenzhen 518120, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifei","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guangdong Ocean University, No. 1 Haida Road, Mazhang District, Zhanjiang 524088, China"},{"name":"Shenzhen Institute of Guangdong Ocean University, No. 3 Binhai 2nd Road, Dapeng New District, Shenzhen 518120, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1093\/czoolo\/58.1.116","article-title":"Why do fish school?","volume":"58","author":"Larsson","year":"2012","journal-title":"Curr. 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