Background <p>Duffing oscillators subjected to complex-frequency excitation exhibit unique dynamic characteristics owing to the additional degree of freedom introduced by the modulation parameter, providing a new approach for tuning system stability and nonlinear resonance behavior.</p> Methods <p>This work investigates a Duffing oscillator under complex-frequency excitation. The method of multiple scales is employed to derive the complex slow-flow equation for the weakly nonlinear system. The analytical solution is further validated using the Galerkin method, demonstrating full consistency between the two approaches. Based on the derived amplitude–frequency relation, the effects of the modulation parameter, damping ratio, and observation time on the steady-state response are systematically analyzed for both hardening and softening spring cases. Time-domain simulations, together with power spectral density and continuous wavelet transform analyses, are performed to characterize the transient and spectral responses.</p> Results <p>The results show that both the sign and magnitude of the modulation parameter μ significantly influence the resonance characteristics and nonlinear frequency shift. The multiple-scales solution accurately predicts both transient growth/decay and steady-state responses, as confirmed by numerical simulations. Furthermore, the power spectral density and continuous wavelet transform reveal pronounced time-dependent spectral evolution induced by complex-frequency excitation, demonstrating the nonstationary nature of the system response.</p> Conclusions <p>This study establishes a consistent analytical and numerical framework for investigating the dynamics of Duffing oscillators under exponentially modulated excitation, providing new insights into stability regulation and nonlinear dynamic responses in systems subjected to complex-frequency excitation.</p>