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Collapse mechanisms of a Neimark–Sacker torus by Alvin Penner is a Physics and Astronomy article available to read on EtoBox.
What is Collapse mechanisms of a Neimark–Sacker torus about?
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. For the first example of collapse, the above two methods yield the same result, namely that the collapse is characterized by a constant rotation number as we move away from the bifurcation, leading to a torus that usually coalesces into discrete branches and then collapses due to turning points. This mechanism allows us to define a simple criterion that the parameters of the cubic model must satisfy, which is related to stability. The second example of collapse is more complex: the normalized cubic
Who reads Collapse mechanisms of a Neimark–Sacker torus?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- Alvin Penner
- Publisher
- Elsevier BV
- Published
- 2023
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)