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

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 (V_{0}), the potential function optimization parameters (b_{h} and c_{h}), driving frequency (ω), and amplitude (F_{0}). 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 I_{2} and Cl_{2} than for CO or O_{2}. Variations in F_{0},b_{h}, and c_{h} had profound impacts on the primary resonance features, with higher F_{0} and lower V_{0} 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 I_{2} and Cl_{2}, driven by large F_{0} at low V_{0}. 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.