The monitoring nodes of the wireless sensor network require an external power supply，and it costs a lot to build and maintain the power supply infrastructure. By using environmental vibration energy to supply power to the monitoring node，it not only saves a lot of investment，but also saves energy and protects the environment，and thus has broad application prospects. However，the state-of-the-art resonant energy harvester has a narrow operating band，and the nonlinear approaches deliver small output power，which is difficult to drive the load circuit. In view of this，this paper proposes a multi-stable nonlinear electromagnetic energy harvesting system and conducts the related experimental study. The fractional-order damping model of the system is established. Experimental research reveals nonlinear behaviors such as dynamic bifurcation，potential well escape，high-energy state orbit，and chaotic motion. The results indicate that Poincaré cross-section stroboscopic sampling algorithm and bifurcation diagram can effectively describe the nonlinear vibration characteristics of the system. The multi-stable electromagnetic system can be utilized to increase the output power and current（i.e. electrical load capacity）of energy harvesters as well as broaden the operating range of frequencies.