Combined Duffing nonlinearity and Bliman–Sorine friction dynamics in rubber bearings

The forced harmonic oscillator with combined Duffing cubic stiffness and Bliman–Sorine dynamic friction model is analyzed using Poincaré sections and parameter‑space basins of attraction, constructed as functions of two key oscillator parameters: friction stiffness and forcing amplitude. The analysis uncovers several key dynamical features: (i) chaotic behavior is absent when the cubic stiffness term is weak; (ii) chaotic regimes emerge as soon as the cubic stiffness becomes strong; (iii) the parameter space develops strongly entangled basins, reflecting extreme sensitivity of attractor selection to frictional micro‑mechanics; and (iv) variations in the Bliman–Sorine and Duffing parameters induce pronounced topological changes in basins of attraction. These findings provide new insight into the structure of oscillations in systems governed by the combined Bliman–Sorine and Duffing models. Numerical simulations are performed using a variable‑step Adams–Bashforth–Moulton explicit–implicit scheme to ensure reliable long‑time integration.