Diffusive intracellular and extracellular ions induce a gradient electromagnetic field that regulates membrane potential, and energy injection from external stimuli breaks the energy balance between the magnetic and electric fields in a cell. Indeed, any activation of biophysical function and self-adaption of biological neurons may be dependent on energy flow, and synapse connection is controlled to reach energy balance between neurons. When more neurons are clustered and gathered closely, field energy is exchanged and shape formation is induced to achieve local energy balance. As a result, the coexistence of multiple firing modes in neural activities is fostered to prevent the occurrence of bursting synchronization and seizure. In this review, a variety of biophysical neuron models are presented and explained in terms of their physical aspects, and the controllability of functional synapses, formation of heterogeneity, and defects are clarified for knowing the synchronization stability and cooperation between functional regions. These models and findings are summarized to provide new insights into nonlinear physics and computational neuroscience.