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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Bifurcations and Phase-space Structures in KCN Molecular System

Discontinuity, Nonlinearity, and Complexity 14(3) (2025) 607--622 | DOI:10.5890/DNC.2025.09.012

F. Revuelta$^{1}$, F. J. Arranz$^1$, R. M. Benito$^1$, F. Borondo$^{2}$

$^1$ Grupo de Sistemas Complejos, Escuela T'ecnica Superior de Ingenier'i a Agron'omica, Alimentaria y de Biosistemas, Universidad Polit'ecnica de Madrid, Avenida~Puerta de Hierro 2-4, 28040 Madrid, Spain

% $^2$ Departamento de Qu'imica, Universidad Aut'onoma de Madrid, Cantoblanco, 28049 Madrid, Spain

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Abstract

In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of the potential energy surface. As the energy increases, the phase space combines regions with regular %motion with regions with and chaotic motion, %behaviors, a difference that is well captured by the Lagrangian descriptors. %due to the underlying %homoclinic and heteroclinic tangle. We show that the dynamics is mostly governed by the invariant manifolds of the stretch periodic orbits located at the top of one of the energetic barriers of the system. Furthermore, we show a perfect agreement between the bifurcation theory and the differences observed in the phase-space structures %shown by Lagrangian descriptors as the vibrational energy is modified. %the changes in the energy are reponsible for bifurcations in the %periodic orbits of the system, a fact that modifies %the phase space dramatically. The accuracy of our calculations is also assessed by explicit comparison with the invariant manifolds computed using linear dynamics.

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