<p>This paper introduces an enhanced nonlinear piezo-electromagnetic hybrid energy harvester, leveraging the inherent tuning capability of the inerter to enhance energy harvesting performance. The governing equations were derived using Hamilton's principle. Both the Runge–Kutta method and the harmonic balance method were used to solve the differential equations, and the results showed excellent agreement. The linearized method was employed to determine the stability of the harmonic balance solutions and to identify the Hopf and Saddle-Node bifurcation points of the system. A parametric study on system output power and energy harvesting efficiency indicated that the stiffness of the nonlinear spring, the magnitude of the acceleration excitation amplitude, the damping coefficient of the beam, the resistance value of the external resistors, and the inertance of the inerter each have unique effects on the system's energy harvesting performance. Notably, the study on the inerter demonstrated that the additional inertial force can significantly enhance output power and energy recycling efficiency at low frequencies. Additionally, the global bifurcation analysis revealed the presence of periodic, multi-periodic, quasi-periodic, and chaotic responses, as well as their transitions under varying parameter conditions. The introduction of the inerter reduces these bifurcation behaviors and enhances the stability of the system's response. These results may pave the way for future advancements in the field of energy harvesting technology. Please check the edit made in the article title. We have checked the edit made in the article title. It is acceptable for us due to its negligible influence on the scientific meaning of this paper.</p>