<p>The FitzHugh-Nagumo (FHN) neural circuit and its dimensionless model present the main dynamical characteristic of biological neurons, as a result, incorporation of functional electric components enable approach of physical effect in the derived biophysical neuron models. To approach synaptic coupling between neurons, different electric components including resistor, memristor, and even nonlinear resistor can be used to connect the output ends from the neural circuits, and maximal voltage coupling occurs, which the synapses connect the output terminals under maximal output voltage. In this article, three kinds of synaptic couplings are activated to shunt currents from the inductive channels of the FHN neural circuit, respectively, and the voltage division from the inductive branch circuit controls energy exchange along the coupling channel. As a result, two neural circuits are coupled by the shunted voltage and current from each inductive channel, and this scheme avoids to couple two neural circuits under full output voltage from the capacitor. It is different from the previous schemes that bidirectional coupling just applies negative feedback on the membrane potentials directly when neurons are connected by electric, chemical and/or memristive synapse. By performing scale transformation on the physical equations of the coupled neural circuits under different coupling forms, the dimensionless theoretical model of two coupled neurons is established for each case, and the Hamilton energy is derived to reveal the relationship between energy balance and firing dynamics in neural activities. The relationship between coupling strength and synchrony, as well as the influence of synchrony on energy diversity is analyzed. It is revealed that the memristor channel coupling seldom supports energy balance under the voltage division. Stochastic resonance is studied, and it finds that the resistive coupling under voltage division is more sensitive to noise interference. An adaptive control scheme is introduced to effectively regulate the firing mode of neurons, and the influence of the energy threshold on the stable state of neurons is discussed. This study not only reveals the complex dynamical behaviors of neurons under different coupling schemes, including periodic, double-periodic, and chaotic states, but also provides theoretical basis and practical references for the design of current-coupled circuits, adaptive regulation strategies, and the development of brain-inspired information processing systems. </p>