We investigate the nonlinear dynamics of a linearly coupled van der Pol–Duffing system using numerical continuation, time-domain simulations, stochastic analysis, and analog circuit experiments. The model exhibits a rich variety of dynamical regimes, including periodic oscillations, period-doubling cascades, and chaotic attractors arising from the interplay between self-excitation and nonlinear stiffness. Numerical continuation is employed to reconstruct the bifurcation structure, enabling the identification of equilibrium branches, periodic solutions, and their stability in parameter space. The time-domain numerical results reveal the mechanisms governing transitions between regular and chaotic dynamics. To assess robustness under realistic conditions, intrinsic stochastic perturbations are introduced, showing that increasing noise intensity progressively erodes fine periodic structures, while larger dynamical domains remain comparatively robust. Experimental results obtained from an analog circuit implementation confirm the main dynamical regimes predicted numerically. Overall, the combined computational and experimental approach provides a systematic characterization of the system’s bifurcation structure and its robustness to noise. The results support the concept of chaos-based sensing and are consistent with previous findings in chaotic bioimpedance detection, indicating that maximum sensitivity occurs near regions of high bifurcation complexity, where small parameter variations induce significant qualitative changes in the system dynamics.
Prebianca et al. (Wed,) studied this question.
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