A functional neuron has been developed from a simple by incorporating a phototube and a thermistor in different branch circuits. The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor. The firing mode of this neuron is controlled synchronously by external temperature and illumination. There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions. As a result, synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons. We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons. The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons, and the realization of synchronization is helpful in maintaining energy balance between neurons. The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization. The second criterion is that the coupling intensity increases exponentially before reaching energy balance. When two neurons become non-identical, phase synchronization can be controlled during the activation of synapse connections to neurons. For two identical neurons, the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance, even in the presence of noise. This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially. These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli. The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons. These results provide guidance for designing and training intelligent neural networks by taming the coupling channels with gradient energy distribution.