The analysis of the classical Lennard-Jones (LJ) oscillator under harmonic excitation reveals a fascinating phenomenon—a rich interplay between quasi-periodic motion and intermittent chaos. It is shown that chaotic oscillations can emerge even at low forcing amplitudes, while the system remains largely non-chaotic across a broad parameter range. The emergence of strange attractors composed of densely organized regular patterns represents another distinctive and persistent feature of the LJ oscillator. The analysis employs bifurcation diagrams, the largest Lyapunov exponents (LLEs), correlation dimension (CD), Shannon entropy (SE), and other tools. A comparison with the Duffing oscillator reveals a substantial discrepancy in oscillation regimes across the whole range of forcing amplitudes. To ensure numerical stability, the variable-step Adams–Bashforth–Moulton (ABM) method in an explicit–implicit formulation was used.
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