Abstract
It is difficult to explore the induced mechanism of neuronal firing activity and the cooperation between neurons experimentally, so some neuronal circuits are established to train mode transformation and selection. Furthermore, some functional device, for example, piezoelectric ceramic, thermistor, phototube are inset in neuronal circuits and the functional neurons are developed to perceive some specific physical signal. In this paper, a linear resistance and an ideal Josephson junction are parallelly connected to FitzHugh-Nagumo (FHN) neuronal circuit, and then a functional neuron is established to percept the induction currents induced by the external magnetic field. Some basic dynamics are analyzed in terms of two-parameter bifurcation, one-parameter bifurcation and interspike interval(ISI for short) bifurcation, it is indicated that the functional neuron is sensitive to the electromagnetic stimulation and has rich multimodal transformations. The period-adding bifurcations accompanied by multi-period and chaos between two period cascades occupy the entire bifurcation interval when the external magnetic field is given in steady state, while the irregular modal transformations between period and chaos can be observed when the functional neuron encounters a periodic external magnetic field. Furthermore, two functional neurons are bridged with a capacitor, so field coupling is induced, then the effects of coupling strengths on complete synchronization are investigated by calculating the synchronization error function and the bifurcation diagram. In addition, the local dynamics of the network node play an important role in collective behavior and synchronous transition, so two capacitor-coupled functional neurons is presented as the network nodes, and a chain neural network is constructed to explore the effects of external magnetic field and coupling strength on network synchronous behavior. Obviously, the orderliness of the neural network can enhance or destroy under different modulation of external magnetic stimulation and coupling strength. It can give insights to investigate synchronization on neural networks with field coupling and useful guidance for implementing artificial synapse for signal processing.
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