Bifurcation Study on a Degenerate Double van der Waals Cirque Potential Energy Surface using Lagrangian Descriptors

TL;DR

This study investigates the bifurcations of periodic orbits in a Hamiltonian system with a degenerate double van der Waals potential energy surface, using Lagrangian descriptors and Poincaré maps to analyze energy-dependent dynamics.

Contribution

It introduces the application of Lagrangian descriptors to identify bifurcations of periodic orbits in a complex potential energy surface, expanding tools for dynamical systems analysis.

Findings

Lagrangian descriptors effectively detect bifurcations of periodic orbits.

The method distinguishes different types of bifurcations such as saddle-node and pitchfork.

Periodic orbit bifurcations are characterized across energy levels.

Abstract

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 Poincar\'e 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.