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Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle

Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven... In chemical reactions, trajectories typicallyturn from reactants to products when crossing a dividing surfaceclose to the normally hyperbolic invariant manifold (NHIM) given bythe intersection of the stable and unstable manifolds of a rank-1saddle. Trajectories started exactly on the NHIM in principle neverleave this manifold when propagated forward or backward in time.This still holds for driven systems when the NHIM itself becomestime-dependent. We investigate the dynamics on the NHIM for aperiodically driven model system with two degrees of freedom bynumerically stabilizing the motion. Using Poincaré surfaces ofsection, we demonstrate the occurrence of structural changes of thedynamics, viz., bifurcations of periodic transition state (TS)trajectories when changing the amplitude and frequency of theexternal driving. In particular, periodic TS trajectories with thesame period as the external driving but significantly differentparameters — such as mean energy — compared to theordinary TS trajectory can be created in a saddle-node bifurcation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Dynamics and Bifurcations on the Normally Hyperbolic Invariant Manifold of a Periodically Driven System with Rank-1 Saddle

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References (71)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2020
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354720050068
Publisher site
See Article on Publisher Site

Abstract

In chemical reactions, trajectories typicallyturn from reactants to products when crossing a dividing surfaceclose to the normally hyperbolic invariant manifold (NHIM) given bythe intersection of the stable and unstable manifolds of a rank-1saddle. Trajectories started exactly on the NHIM in principle neverleave this manifold when propagated forward or backward in time.This still holds for driven systems when the NHIM itself becomestime-dependent. We investigate the dynamics on the NHIM for aperiodically driven model system with two degrees of freedom bynumerically stabilizing the motion. Using Poincaré surfaces ofsection, we demonstrate the occurrence of structural changes of thedynamics, viz., bifurcations of periodic transition state (TS)trajectories when changing the amplitude and frequency of theexternal driving. In particular, periodic TS trajectories with thesame period as the external driving but significantly differentparameters — such as mean energy — compared to theordinary TS trajectory can be created in a saddle-node bifurcation.

Journal

Regular and Chaotic Dynamics – Springer Journals

Published: Sep 28, 2020

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