<p>In this paper, we propose a bistable piezoelectric vibration energy harvesting system integrated with a magnetic flux-controlled memristor (MFCM), and develop its corresponding theoretical dynamical model. The dynamical characteristics of the model are investigated, and several performance metrics including signal-to-noise ratio, instantaneous output voltage, average output voltage, and energy harvesting efficiency, are evaluated via numerical simulations. The results indicate that under moderate ambient noise conditions, the system can achieve relatively high firing frequency and energy harvesting efficiency. Adding the MFCM appears to improve the output power and the energy harvesting efficiency to some extent. Specifically, the memristor parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha '\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>α</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> has a moderate influence on the efficiency, while <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta '\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> shows negligible effect. The electromechanical coupling coefficient <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> affects the output power as expected. The inclusion of the MFCM also introduces additional tunable parameters that may help optimize performance. For better energy harvesting performance, a balance among noise intensity, firing frequency, and circuit output power seems important under the conditions studied. These findings may provide a useful reference for designing tire vibration energy harvesters.</p>