This paper investigates the influence of rough-driven potentials on harmonically forced Duffing-van der Pol oscillators, focusing on both biharmonically and bistably forced \(\phi ^6\) oscillators. We analyze the emergence of primary resonances, hierarchical structures, and strange attractors by varying roughness and nonlinear parameters. The system’s dynamics are explored through bifurcation diagrams, Lyapunov exponents, and Poincaré cross-sections. Results reveal complex resonance behaviors, characterized by multiple resonance peaks, periodic-chaotic transitions, and structural instabilities induced by fine-scale roughness. The findings offer insights into the role of roughness in nonlinear oscillators, with potential implications in physics, engineering, and signal processing.
