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As the main research tool we used the method of Lyapunov exponents charts. For coupled systems, the possibility of two-, three- and four-frequency quasi-periodicity is revealed. Illustrations in the form of Fourier spectra are presented. Doublings of invariant curves, two- and three-dimensional tori are found. The transition from two-dimensional tori to three-dimensional ones occurs through a quasi-periodic saddle-node bifurcation of invariant tori or through a quasi-periodic Hopf bifurcation. A discrete version of the hyperchaotic R\u00f6ssler oscillator is also discussed. It exhibits dynamical behavior close to a flow system in some measure. <\/jats:p>","DOI":"10.1142\/s0218127423300379","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T06:08:11Z","timestamp":1702361291000},"source":"Crossref","is-referenced-by-count":5,"title":["Discrete R\u00f6ssler Oscillators: Maps and Their Ensembles"],"prefix":"10.1142","volume":"33","author":[{"given":"Alexander P.","family":"Kuznetsov","sequence":"first","affiliation":[{"name":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7843-646X","authenticated-orcid":false,"given":"Yuliya V.","family":"Sedova","sequence":"additional","affiliation":[{"name":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"}]},{"given":"Nataliya V.","family":"Stankevich","sequence":"additional","affiliation":[{"name":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering and Electronics of Russian Academy of Sciences, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"},{"name":"Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics, Bolshaya Pecherskaya Str., 25\/12, Nizhny Novgorod 603155, Russian Federation"}]}],"member":"219","published-online":{"date-parts":[[2023,12,11]]},"reference":[{"key":"S0218127423300379BIB001","first-page":"108","volume":"21","author":"Adilova A. 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