Synchronization characteristics of functional neurons under energy control

In biological neurons, synapses receive external stimuli to induce firing patterns. While the rapid generation of synapses regulates neural activity. In this paper, we use a magnetic-flux controlled memristor (MFCM) as a synapse to connect two functional neurons, establish the new coupled neurons, and study the synchronization characteristics. Firstly, we connect two neurons using memristive synapses, and derive the equations of the coupled neurons based on Kirchhoff's voltage law. Furthermore, we calculate the energy of the memristive coupling channels, and obtain the energy difference between the coupled neurons. Secondly, we propose a criterion for exponential growth controlled by energy difference. By setting higher coupling channel strength to establish synaptic connections, energy pumping can be effectively activated. Finally, for three modes, we analyze the energy evolution under the variations of memristive synapses, and find that the coupling channels are adaptively controlled by energy difference. The results show that when the coupling strength through synapses is enhanced, identical neurons can achieve complete synchronization, and different neurons can achieve phase locking. This study clarifies the underlying mechanisms of regulating coupled neurons via memristive synapses and explores how neurons achieve potential energy balance from the perspective of physical fields.