<p>Dynamical models that emphasize important features and downplay the inessential details have been proposed and developed in neuroscience and biomathematics. Given the major properties of pyramidal neurons and the energy diversities in different cells, a bi-membrane neuron-like model with two cells is proposed to reproduce bursting modes. The two cell circuits are connected by a resistive switching and a memristive coupling associated with the energy flow, respectively. The generation mechanism of bursting is explained by using the fast-slow decomposition and numerical method. Based on the bifurcation and inter-spike interval, it is found that the firing patterns can exhibit different transitions under resistive switching and memristive coupling. Finally, the firing patterns of the bi-membrane neuron-like model are demonstrated by the implementation of a hardware circuit. The bi-membrane neuron model plays a significant important impact in the generation and transition of electrical activities.</p>