Collapse mechanisms of a Neimark–Sacker torus

Alvin Penner

Chaos, Solitons & Fractals, 2023, vol. 169, issue C

Abstract: Two examples of collapse of a Neimark–Sacker torus in the Rössler system are studied. Their stability is evaluated by measuring the rotation number, defined as the long-term average value of the angular phase shift that occurs in the Poincaré map on each pass, and by theoretically calculating the same angular shift within the context of a normalized cubic model. The parameters of the cubic model are evaluated using perturbation theory applied to a limit cycle, which involves first evaluating the response after a fixed time, the known period of the limit cycle, and then calculating the additional effect due to variations in time of flight to reach a fixed plane perpendicular to velocity.

Keywords: Rössler equations; Neimark–Sacker; Torus; Phase portrait; Poincaré map; Bifurcation; Limit cycle; Rotation number (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923002047

DOI: 10.1016/j.chaos.2023.113303

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