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We show that this system exhibits strange spiral attractors (Shilnikov attractors) with two zero (indistinguishable from zero in numerics) Lyapunov exponents in a wide region of the parameter space. We explain this phenomenon by means of bifurcation analysis of a three-dimensional Poincar\u00e9 map for the system under consideration. We show that chaotic dynamics develop here near a codimension three bifurcation, when a periodic orbit (fixed point of the Poincar\u00e9 map) has the triplet of multipliers (1,1,1). As it is known, the flow normal form for such bifurcation is the well-known three-dimensional Arneod\u00f3\u2013Coullet\u2013Spiegel\u2013Tresser (ACST) system, which exhibits spiral attractors. According to this, we conclude that the additional zero Lyapunov exponent for orbits in the observed attractors appears due to the fact that the corresponding three-dimensional Poincar\u00e9 map is very close to the time-shift map of the ACST-system.<\/jats:p>","DOI":"10.1063\/5.0098163","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T16:47:41Z","timestamp":1662655661000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":15,"title":["On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators"],"prefix":"10.1063","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3316-8841","authenticated-orcid":false,"given":"Evgeny A.","family":"Grines","sequence":"first","affiliation":[{"name":"Lobachevsky State University of Nizhni Novgorod 1 , 23 Gagarin av., Nizhny Novgorod 603950, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0002-6553","authenticated-orcid":false,"given":"Alexey","family":"Kazakov","sequence":"additional","affiliation":[{"name":"National Research University Higher School of Economics 2 , 25\/12 Bolshaya Pecherskaya Ulitsa, 603155 Nizhny Novgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3551-471X","authenticated-orcid":false,"given":"Igor R.","family":"Sataev","sequence":"additional","affiliation":[{"name":"Kotelnikov\u2019s Institute of Radio-Engineering and Electronics of RAS 3 , Saratov Branch, Zelenaya 38, Saratov 410019, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2022,9,8]]},"reference":[{"key":"2023080921195813800_c1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.20537\/nd1201001","article-title":"Towards scenarios of chaos appearance in three-dimensional maps","volume":"8","year":"2012","journal-title":"Rus. 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