Energy dependence on modes of electric activities of neuron driven by multi-channel signals

Neuron can receive electric signals or forcing currents from more than one channel, and these forcing currents could show some diversity. Based on the Hindmarsh-Rose neuron model, mixed forcing currents, which are composed of low-frequency, high-frequency and constant signals, are imposed on the neuron, and multiple modes of electric activities could be observed alternately (in turn) from the neuron. Based on the Helmholtz theorem, the Hamilton energy is calculated to discern the energy dependence on the mode selection of the electric activities of neuron. It is found that the response of electrical activities much depends on the amplitude than the frequency when mixed signals are imposed on the neuron synchronously; however, the rhythm of electrical activities could be adjusted by the frequency of the periodical signals in the mixed signal. It is confirmed that the energy is much dependent on the mode of electrical activities instead of the external forcing currents directly, and a smaller energy occurs under bursting states. The delayed response of Hamilton energy to external forcing currents confirms that neuron contributes to energy coding. These results could be helpful for further investigation on energy problems in neuronal network associated with model transition for collective behaviors.