Numerically Bounded Chaos in a Driven Double-Well Duffing Oscillator

This paper presents a reproducible numerical study of bounded chaotic dynamics in a minimal driven nonlinear system based on the periodically forced double-well Duffing oscillator. Through numerical integration, phase-space analysis, Poincaré sections, bifurcation scanning, power spectra, and Lyapunov exponent estimation, the study illustrates how deterministic chaos can coexist with long-term spatial confinement in a dissipative system. Using a reference parameter set (δ = 0.25, γ = 0.30, ω = 1.0), the simulations show the emergence of a bounded strange attractor with positive maximal Lyapunov exponent (λmax ≈ 0.118) while trajectories remain globally confined. The work is intended as a reproducible case study in nonlinear dynamics and should be interpreted as a methodological and conceptual contribution rather than a predictive model of any specific physical system. The repository includes the manuscript and is intended to support transparency, reproducibility, and further exploration of bounded chaos in low-dimensional driven systems.