Phase synchronization between neurons under nonlinear coupling via hybrid synapse

Biological neurons and nonlinear circuits contain certain inner field energy, and an equivalent Hamilton energy function can be obtained to discern the dependence of firing modes on the energy flow. In this paper, a voltage-controlled resistor is used to connect two neural circuits, and hybrid synapse is activated to control the synchronization stability and mode transition in neurons under phase lock. Realistic stimuli can be combined signals within certain frequency band rather than simple periodic stimulus, and the firing patterns will show multiple modes by applying mixed signals. Similar coherence resonance is detected in an isolated neuron driven by the filtered signals. Therefore, chaotic signals are encoded to represent filtered waves with finite frequency band, and then the mixed signals are used to excite two neural circuits via nonlinear coupling. Hamilton energy for the coupled neurons via hybrid synapse is estimated to detect the controllability of synchronization between neurons. The nonlinear resistor along the coupling channel can reproduce the biophysical property of hybrid synapse accompanying with field coupling, which mainly contributes the energy exchange between neurons. It is confirmed that this hybrid synapse is effective to control the synchronization stability and phase lock even the neurons presenting with different firing patterns/modes. The results confirmed that nonlinear coupling via specific components is helpful to design hybrid synapse, and it is effective to block the bursting synchronization between neurons driven by filtered chaotic signals. Therefore, activation of this hybrid synapse can prevent the occurrence of seizure in nervous system.