Bifurcation study on a degenerate double van der Waals cirque potential energy surface using Lagrangian descriptors

• Published in: Communications in nonlinear science & numerical simulation Vol. 105; p. 106089
• Main Authors: Katsanikas, Matthaios, Sanjuan, Broncio Aguilar, Montoya, Francisco González, García-Garrido, Víctor J., Wiggins, Stephen
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2022; Elsevier Science Ltd
• Subjects: Bifurcations; Bifurcations of periodic orbits; Dynamical systems; Energy; Energy of dissociation; Free energy; Hamiltonian functions; Heat of formation; Lagrange multiplier; Lagrangian descriptors; Mathematical models; Orbits; Phase space structure; Poincare maps; Potential energy; Lagrangian descriptors; Bifurcations of periodic orbits; Phase space structure
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2021.106089

In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the dissociation energy, which occurs when the system becomes open. In particular, we study the bifurcations of the basic families of periodic orbits of this system as the energy increases using Lagrangian descriptors and Poincaré maps. We investigate the capability of Lagrangian descriptors to find periodic orbits of bifurcating families for the case of resonant, saddle–node and pitchfork bifurcations. •Study of a degenerate double van der Waals potential energy surface.•Detection of periodic orbits with Lagrangian descriptors.•Detection of bifurcations of periodic orbits using Lagrangian descriptors.•Visualization and detection of resonant zones and resonant bifurcations using Lagrangian descriptors.