{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:48:08Z","timestamp":1773794888483,"version":"3.50.1"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p> In this paper, we construct the polytope which contains all compact \u03c9-limit sets of the four-dimensional R\u00f6ssler system which is a generalization of the hyperchaotic R\u00f6ssler system for the case of positive parameters. Further, we find a few three-dimensional planes containing all compact \u03c9-limit sets for bounded positive half-trajectories located in some subdomains in the half-space z &gt; 0. Besides, we analyze one case in which all compact \u03c9-limit sets in the half-space z &gt; 0 are contained in one three-dimensional plane. Our approach is based on a combination of the LaSalle theorem and the extreme-based localization method of compact invariant sets. <\/jats:p>","DOI":"10.1142\/s0218127414501491","type":"journal-article","created":{"date-parts":[[2014,11,28]],"date-time":"2014-11-28T16:50:32Z","timestamp":1417193432000},"page":"1450149","source":"Crossref","is-referenced-by-count":7,"title":["On the Ultimate Dynamics of the Four-Dimensional R\u00f6ssler System"],"prefix":"10.1142","volume":"24","author":[{"given":"Konstantin E.","family":"Starkov","sequence":"first","affiliation":[{"name":"Instituto Politecnico Nacional, CITEDI, Av. 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