Hamilton energy modulation and synchronization control for a kind of coupled function neurons

Artificial neural circuits can effectively reproduce the main biophysical properties of neurons when reliable electronic components with unique physical properties are introduced. Connecting memristor to neural circuits not only enhances the potential controllability under external physical stimuli but also recognizes the effects of electromagnetic induction on neural activity. In this paper, the piezoelectric ceramic and memristor are embedded in FitzHugh-Nagumo (FHN) neural circuit, then two kinds of functional neuron models with magnetic field-control and electric field-control are obtained, respectively, to estimate the effects of external sound waves and external electric fields. To investigate the energy consumption when information transfer between neurons, the Hamilton energy functions of the above neuron models are obtained by calculating the field energy of each electronic component, and their correctness is verified by Helmholtz’s theorem. In addition, two neurons can be coupled by an induction coil to equal the processing of chemical coupling and realize pumping energy between neurons. Moreover, an energy switch is added to the coupling channel to open or close the coupling channel by detecting the diversity of energy. That is, it is kept open when the coupled system is exchanging field energy until the energy diversity between neurons is controlled at a limited threshold. The two-parameter bifurcation results show that the above two neurons have different bifurcation modes under different external magnetic or electric fields. For coupled systems, it is found that two identical neurons can achieve complete synchronization (energy balance) or intermittent complete synchronization (intermittent energy balance) by adaptive coupling. However, two diverse neurons can only achieve phase lock or phase synchronization, since the diversity of the coupled system parameters can disrupt the achievement of complete synchronization. These results are helpful for designing intelligent neural networks by taming the coupling channels with gradient energy distribution.