Connecting memristors into any neural circuit can enhance its potential controllability under external physical stimuli. Memristive current along a magnetic flux-controlled memristor can estimate the effect of electromagnetic induction on neural circuits and neurons. Here, a charge-controlled memristor is incorporated into one branch circuit of a simple neural circuit to estimate the effect of an external electric field. The field energy kept in each electric component is respectively calculated, and equivalent dimensionless energy function H is obtained to discern the firing mode dependence on the energy from capacitive, inductive, and memristive channels. The electric field energy HM in a memristive channel occupies the highest proportion of Hamilton energy H, and neurons can present chaotic/periodic firing modes because of large energy injection from an external electric field, while bursting and spiking behaviors emerge when magnetic field energy HL holds maximal proportion of Hamilton energy H. The memristive current is modified to control the firing modes in this memristive neuron accompanying with a parameter shift and shape deformation resulting from energy accommodation in the memristive channel. In the presence of noisy disturbance from an external electric field, stochastic resonance is induced in the memristive neuron. Exposed to stronger electromagnetic field, the memristive component can absorb more energy and behave as a signal source for energy shunting, and negative Hamilton energy is obtained for this neuron. The new memristive neuron model can address the main physical properties of biophysical neurons, and it can further be used to explore the collective behaviors and self-organization in networks under energy flow and noisy disturbance.
