Contingencies, such as behavior shifts of microgrid operators (MGOs) and abrupt weather fluctuations, significantly impact the economic operations of multi-microgrids (MMGs). To address these contingencies and enhance the economic and autonomous performance of MGOs, a self-organizing energy management modeling approach is proposed. A second-order stochastic dynamical equation (SDE) is developed to accurately characterize the self-organizing evolution of the operating cost of MGO incurred by contingencies. Firstly, an operating model of MMG relying on two random graph-driven information matrices is constructed and the order parameters are introduced to extract the probabilistic properties of variations in operating cost. Subsequently, these order parameters, which assist individuals in effectively capturing system correlations and updating state information, are incorporated as inputs into second-order SDE. The second-order SDE is then solved by using the finite difference method (FDM) within a loop-structured solution framework. Case studies conducted within a practical area in China validate that the proposed self-organizing energy management model (SEMM) demonstrates spontaneous improvements in economic performance compared with conventional models.