{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T11:36:59Z","timestamp":1763552219198,"version":"3.41.2"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p> We derive a closed analytical form of planar rotational equilibria that exist in the three-dimensional motion of two hydrodynamically coupled nonidentical microswimmers, each modeled as a force dipole with intrinsic self-propulsion. Using the method of images for zero Reynolds number flows near interfaces, we demonstrate that our results remain equally applicable at a stress-free liquid\u2013gas interface as in the bulk of a fluid. For a pair of two pullers and a pair of two pushers the linear stability of the equilibria is analyzed with respect to two- and three-dimensional perturbations. A universal stability diagram of the orbits with respect to two-dimensional perturbations is constructed and it is shown that two nonidentical pushers or two nonidentical pullers moving at a stress-free interface may form a stable rotational equilibrium. For two nonidentical pullers we find stable quasi-periodic localized states, associated with the motion on a two-dimensional torus in the phase space. Stable tori are born from the circular periodic orbits as the result of a torus bifurcation. All stable equilibria in two dimensions are shown to be monotonically unstable with respect to three-dimensional perturbations. <\/jats:p>","DOI":"10.1142\/s021812742230021x","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T09:06:22Z","timestamp":1659085582000},"source":"Crossref","is-referenced-by-count":1,"title":["Planar Rotational Equilibria of Two Nonidentical Microswimmers"],"prefix":"10.1142","volume":"32","author":[{"given":"Prajitha","family":"Mottammal","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumesh P.","family":"Thampi","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrey","family":"Pototsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"S021812742230021XBIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.045302"},{"key":"S021812742230021XBIB002","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms9396"},{"key":"S021812742230021XBIB003","series-title":"Encyclopaedia of Mathematical Sciences","volume-title":"Dynamical Systems V: Bifurcation Theory and Catastrophe Theory","author":"Arnold V.","year":"2013"},{"key":"S021812742230021XBIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112070000745"},{"key":"S021812742230021XBIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.031104"},{"key":"S021812742230021XBIB006","doi-asserted-by":"publisher","DOI":"10.1063\/1.2894480"},{"key":"S021812742230021XBIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.228102"},{"key":"S021812742230021XBIB009","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.061914"},{"key":"S021812742230021XBIB010","doi-asserted-by":"publisher","DOI":"10.1002\/andp.19223731003"},{"key":"S021812742230021XBIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(88)80274-1"},{"key":"S021812742230021XBIB012","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198507239.001.0001"},{"key":"S021812742230021XBIB013","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.02537"},{"key":"S021812742230021XBIB014","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112006002631"},{"key":"S021812742230021XBIB015","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/72\/9\/096601"},{"key":"S021812742230021XBIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-81-322-2556-0"},{"key":"S021812742230021XBIB017","doi-asserted-by":"publisher","DOI":"10.1063\/1.5111296"},{"key":"S021812742230021XBIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S021812742030013X"},{"key":"S021812742230021XBIB019","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-009-9479-6"},{"key":"S021812742230021XBIB020","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-21832-w"},{"key":"S021812742230021XBIB021","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.6.094004"},{"key":"S021812742230021XBIB022","doi-asserted-by":"publisher","DOI":"10.1007\/BF01940759"},{"key":"S021812742230021XBIB023","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.228103"},{"key":"S021812742230021XBIB024","doi-asserted-by":"publisher","DOI":"10.1137\/040611240"},{"key":"S021812742230021XBIB025","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.158102"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812742230021X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T09:09:07Z","timestamp":1659085747000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S021812742230021X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7]]},"references-count":24,"journal-issue":{"issue":"09","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["10.1142\/S021812742230021X"],"URL":"https:\/\/doi.org\/10.1142\/s021812742230021x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2022,7]]},"article-number":"2230021"}}