Energy estimation and coupling synchronization between biophysical neurons

Static charges can induce spatial electric field while moving charges can induce magnetic field. As a result, continuous pumping and exchange of intercellular and extracellular Calcium, potassium and sodium of cells will generate time-varying magnetic field in the media. Therefore, the physical effect of electromagnetic induction in neural activities should be included in building biological neurons. On the other hand, the occurrence of action potential and propagation of ions require energy consumption and supply, so the estimation of physical energy becomes important. Based on our memristive biophysical neuron model, the Hamilton energy function is obtained by using the Helmholtz's theorem, and this energy is contributed by the electric field and magnetic field described by magnetic flux. It is found that this improved neuron model can present the main dynamical properties in neural activities, and it characterizes the lower threshold behavior and subthreshold oscillation during refractory period. The external forcing current on an isolate is adjusted to calculate the firing patterns, energy function and mode transition, which shows the dependence of energy on electrical activities. Finally, magnetic coupling is triggered to modulate the phase synchronization between two identical neurons connected by electric synapse, respectively.