Introduction <p>In this article, a quasi-zero stiffness energy harvesting system with an inertial amplifier is proposed. The device has adjustable performance and can adjust the intrinsic frequency of the system by varying the dynamic effective mass of the system. </p> Materials and methods <p>The amplitude-frequency response equations and curves of the system when it is in the resonance state are obtained using the multi-scale method. In addition, the image of the system’s basin of attraction is plotted in terms of the system’s Lyapunov exponent, and the trajectory changes and energy harvesting changes of the system are investigated for different initial value states.</p> Results <p> The results show that changes in the initial angle of the inertial amplification device will cause changes in the resonance frequency band of the system, and the energy collection efficiency of the system in the ultra-low frequency band can be improved by reasonably adjusting the initial angle of the inertial amplification device.</p> Conclusion <p> The coexistence basins of attraction of the system can give a very good identification scheme, which can greatly improve the energy harvesting efficiency within a certain range.</p>