{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T18:04:45Z","timestamp":1791569085551,"version":"4.3.4"},"reference-count":32,"publisher":"AIP Publishing","issue":"8","funder":[{"name":"Statement assignment of Kotelnikov IREE of RAS","award":["FFWZ-2025-0016"],"award-info":[{"award-number":["FFWZ-2025-0016"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:p>A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within these regions. Among them, structures known for periodic regimes as \u201cshrimps\u201d stand out. Within quasi-periodic shrimps, there are numerous bifurcations of doubling invariant tori, leading to a transition to chaos. The Poincar\u00e9 sections for different quasi-periodic windows correspond to invariant curves with distinct numbers of turns.<\/jats:p>","DOI":"10.1063\/5.0334000","type":"journal-article","created":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T13:04:16Z","timestamp":1786971856000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Quasi-periodic structures and \u201cshrimps\u201d in chaos on the example of a two-mode van der Pol generator"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5528-1979","authenticated-orcid":false,"given":"Alexander P.","family":"Kuznetsov","sequence":"first","affiliation":[{"name":"Laboratory of Theoretical Nonlinear Dynamics, Kotel\u2019nikov's Institute of Radio-Engineering and Electronics of RAS 1 , Saratov Branch, Zelenaya 38, Saratov 410019,","place":["Russian Federation"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3551-471X","authenticated-orcid":false,"given":"Igor R.","family":"Sataev","sequence":"additional","affiliation":[{"name":"Laboratory of Theoretical Nonlinear Dynamics, Kotel\u2019nikov's Institute of Radio-Engineering and Electronics of RAS 1 , Saratov Branch, Zelenaya 38, Saratov 410019,","place":["Russian Federation"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4781-0567","authenticated-orcid":false,"given":"Nataliya V.","family":"Stankevich","sequence":"additional","affiliation":[{"name":"Laboratory of Topological Methods in Dynamics, HSE University 2 , Bolshaya Pecherskaya str. 25\/12, Nizhny Novgorod 603155,","place":["Russian Federation"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,8,17]]},"reference":[{"issue":"4","key":"2026081709041084500_c1","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1002\/cta.4490220404","article-title":"Chua\u2019s circuit 10 years later","volume":"22","year":"1994","journal-title":"Int. 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