Energy level transition and mode transition in a neuron

During continuous diffusion and propagation of intracellular ions, energy transition between electric and magnetic field is proceeded to present appropriate firing patterns. For theoretical neuron models, an equivalent Hamilton energy is derived by Helmholtz theorem. For neural circuits, the Hamilton energy can also be obtained by applying scale transformation on the field energy function. External stimuli injects energy into the neuron, and the energy level transition is induced accompanying with mode transition in the neuronal activity. On the flip side, large external stimuli can induce shape deformation of the cell and possible parameter shift occurs to keep neuron on appropriate energy level in the deterministic neuron models. In this letter, energy function for Hindmarh–Rose neuron is estimated and a criterion for transition between energy levels and firing modes is defined and explained. It provides possible clues for understanding the dependencies of pattern selection in discharge mode on energy level and adaptive controllability in neurons, and thus the neural activities in neurons and nervous system can be controlled by regulating energy flow.