Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors

Shibabrat Naik*, Víctor J. García-Garrido, Stephen Wiggins

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)
29 Downloads (Pure)


Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, and their stable and unstable manifolds have been an integral part of computing quantitative results such as the transition fraction, rate of stability basin erosion in multi-stable mechanical systems, and rate constants in chemical reactions. Thus, methods that can reveal the geometry of these invariant manifolds in high dimensional phase space (4 or more dimensions) need to be benchmarked by comparing with known results. In this study we assess the capability of one such method called Lagrangian descriptor for revealing the types of high dimensional phase space structures associated with an index-1 saddle in Hamiltonian systems. The Lagrangian descriptor based approach is applied to two and three degree-of-freedom quadratic Hamiltonian systems where the high dimensional phase space structures are known, that is as closed-form analytical expressions. This leads to a direct comparison of features in the Lagrangian descriptor contour maps and the phase space structures’ intersection with an isoenergetic two-dimensional surface, and hence provides a verification of the method.

Original languageEnglish
Article number104907
Number of pages34
JournalCommunications in Nonlinear Science and Numerical Simulation
Early online date3 Jul 2019
Publication statusPublished - 1 Dec 2019


  • Chemical reaction dynamics
  • Hamiltonian systems
  • Lagrangian descriptors
  • Normally hyperbolic invariant manifolds
  • Phase space transport
  • Stable and unstable manifolds

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