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Complex dynamics and multistability of driven diatomic molecules revealed by numerical modeling of shifted molecular potentials

O. T. Kolebaje1,*, U. E. Vincent2,3,†, and P. V. E. McClintock3

  • *Contact author: olusolakolebaje2008@gmail.com
  • †Contact author: u.vincent@lancaster.ac.uk
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Phys. Rev. E 112, 044207 – Published 7 October, 2025

DOI: https://doi.org/10.1103/2pvr-llm9

Abstract

We have explored the nonlinear dynamics of six common, driven, diatomic molecules using a shifted Tietz-Wei (sTW) model of their molecular potential functions. We focused on the variations in their resonances, bifurcations and multistability with changes in the spectroscopic and driving force parameters, namely the dissociation energy (V0), the potential function optimization parameters (bh and ch), driving frequency (ω), and amplitude (F0). We used the method of multiple timescales to obtain frequency response curves for the primary and secondary superharmonic resonances. The primary resonances were larger for I2 and Cl2 than for CO or O2. Variations in F0,bh, and ch had profound impacts on the primary resonance features, with higher F0 and lower V0 enhancing the response amplitude. Evidence for hysteresis in the frequency-response—a signature of multistability—is demonstrated. Superharmonic resonances are marked by increased amplitudes and significant hysteresis, especially for I2 and Cl2, driven by large F0 at low V0. Bifurcation diagrams, maximal Lyapunov exponents, and Poincaré maps were used to unravel the transitions between periodic and chaotic states. Period-doubling bifurcations, sudden chaos, and an abundance of crisis events, viz boundary, interior, and attractor-merging crises, were identified as the routes to a range of different chaotic states. Symmetry-breaking, attractor-bubbling, and multistability were all found and are reported. Coexisting attractors and their basins of attraction showed striped, fractal, and Wada-like basin structures. The results highlight the complex dynamics stemming from the interaction between spectroscopic properties and external excitations of the sTW oscillator in diatomic molecules. They carry significant implications for experimental applications.

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Phys. Rev. E 112, 044207– Published 7 October, 2025
  • Received 2 March 2025
  • Accepted 19 September 2025
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