Armstrong-Hélouvry friction oscillator: Emergence of entangled chaotic and multiperiodic structures in parameter space

Forced harmonic oscillators with Armstrong-Hélouvry friction are analyzed using Poincaré sections and parameter-space basins of attraction, constructed as functions of two parameters of this friction model under fixed initial conditions. The study reveals several notable dynamical features: (i) tongue-like regions of chaotic attractors reminiscent of Arnold tongues associated with periodic responses; (ii) chaotic regimes with fractal basin boundaries; (iii) the emergence of entangled basins in parameter space, indicating extreme sensitivity of attractor selection to frictional micro-mechanics; and (iv) pronounced topological changes in Poincaré sections induced by variations in the Armstrong-Hélouvry parameters. These findings provide new insight into the structure of oscillations in systems governed by the Armstrong-Hélouvry friction model. Numerical simulations are performed using a variable-step Adams–Bashforth–Moulton explicit–implicit scheme combined with multiprecision arithmetic to ensure reliable long-time integration.