Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms. The electrophysiological environment inside and outside of the nerve cell is different. Given the continuous and periodical properties of electromagnetic fields in the cell during its working, electronic components involving two capacitors and a memristor are effective in mimicking the physical features. In this paper, a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance. It is found that the memristive neural circuit can present abundant firing patterns without stimulus. The Hamilton energy function is deduced by using the Helmholtz theorem. Further, the neuronal network consisting of memristive neurons is proposed by introducing energy coupling. The controllability and flexibility of parameters make the model have the ability to describe the dynamics and synchronization behaviors.