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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle
Manuel Kuchelmeistera, Johannes Reiffa, Jörg Maina, Rigoberto Hernandezbc a Institut für Theoretische Physik I, Universität Stuttgart,
70550 Stuttgart, Germany
b Johns Hopkins University, Baltimore
c Departments of Chemical \& Biomolecular Engineering,
and Materials Science and Engineering, Johns Hopkins University,
Baltimore, 21218 Maryland, United States
Аннотация:
In chemical reactions, trajectories typically turn from reactants to products when crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given by the intersection of the stable and unstable manifolds of a rank-1 saddle. Trajectories started exactly on the NHIM in principle never leave this manifold when propagated forward or backward in time. This still holds for driven systems when the NHIM itself becomes timedependent. We investigate the dynamics on the NHIM for a periodically driven model system with two degrees of freedom by numerically stabilizing the motion. Using Poincaré surfaces of section, we demonstrate the occurrence of structural changes of the dynamics, viz., bifurcations of periodic transition state (TS) trajectories when changing the amplitude and frequency of the external driving. In particular, periodic TS trajectories with the same period as the external driving but significantly different parameters — such as mean energy — compared to the ordinary TS trajectory can be created in a saddle-node bifurcation.
Ключевые слова:
transition state theory, rank-1 saddle, normally hyperbolic invariant manifold, stroboscopic map, bifurcation.
Поступила в редакцию: 13.07.2020 Принята в печать: 09.09.2020
Образец цитирования:
Manuel Kuchelmeister, Johannes Reiff, Jörg Main, Rigoberto Hernandez, “Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle”, Regul. Chaotic Dyn., 25:5 (2020), 496–507
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1079 https://www.mathnet.ru/rus/rcd/v25/i5/p496
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Страница аннотации: | 96 | Список литературы: | 14 |
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