Energy dependence on the electric activities of a neuron

A nonlinear circuit can be designed by using inductor, resistor, capacitor and other electric devices, and the electromagnetic field energy can be released from the circuit in the oscillating state. The generation of spikes or bursting states in neurons could be energetically a costly process. Based on the Helmholtz's theorem, a Hamilton energy function is defined to detect the energy shift induced by transition of electric modes in a Hindmarsh-Rose neuron. It is found that the energy storage is dependent on the external forcing, and energy release is associated with the electric mode. As a result, the bursting state and chaotic state could be helpful to release the energy in the neuron quickly.