Abstract <p>A comparative analysis of numerical finite difference solvers for the Duffing oscillator with a triple-well potential, shows that the topology of both phase portraits and Poincaré sections depends significantly on the solver, making the problem of choosing the right solver critically important. It is also revealed that all explicit solvers produce similar Poincaré sections, differing from the Poincaré sections produced by implicit solvers. An additional observation pertains to the sensitivity of the Poincaré sections to the frequency of the harmonic excitation. In the periodic regime, all numerical solvers yield nearly indistinguishable Poincaré sections (maps), whereas in the chaotic regime, solver-specific characteristics significantly influence the resulting Poincaré section structures.</p>