<p>This study evaluates the performance of a compressive-mode vibration energy harvester with a flextensional actuator from the viewpoint of global dynamics. According to static analysis of the energy harvester dynamic system, the monostable and bistable potential wells are configured under different values of the initial distance between the magnets. The extended averaging method is utilized to analyze the intra-well and inter-well periodic responses in the bistable case. Numerical results agree well with the theoretical ones. According to the comparisons of the dynamical behaviors under different values of the initial distance, it is found that the initial distance to configure the shallowest double wells is the most efficient in harvesting vibration energy under the low-frequency or low-level ambient excitation. Variations of the coexisting attractors and basins of attraction (BAs) with the increase in the excitation strength are presented, indicating that inter-well periodic and complex responses can be induced by the rise in the excitation amplitude. With the rise in the excitation amplitude, nonlinear phenomena such as rare attractors, hidden attractors, higher-order periodic attractors, chaos, and fractal BAs can be observed.</p>