Phase coupling synchronization of FHN neurons connected by a Josephson junction
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ase coupling synchronization of FHN neurons connected by a Josephson junction 1
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ZHANG Yin , WANG ChunNi , TANG Jun , MA Jun
1,3*
& REN GuoDong
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Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China; School of Physics, China University of Mining and Technology, Xuzhou 221116, China; School of Science, Chongqing University of Posts and Telecommunications, Chongqing 430065, China 2
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Received December 28, 2019; accepted February 22, 2020; published online April 14, 2020
A variety of nonlinear circuits can be tamed to reproduce the main dynamical properties in neural activities for biological neurons while designing reliable artificial synapses for connecting these neural circuits becomes a challenge. In this paper, a Josephson junction is used to build coupling channel for connecting two FitzHugh-Nagumo neural circuits driven by periodical voltage source. The hybrid synapse is designed by using a linear resistor paralleled with a Josephson junction, which can estimate the effect of external magnetic field by generating additive phase error between the junction. Indeed, it activates nonlinear coupling due to phase diversity in the Josephson junction. The coupled circuits are estimated in dimensionless dynamical systems by applying scale transformation on the variables and parameters in neural circuits. In fact, the intrinsic parameters of coupling channel are adjusted to detect the occurrence of synchronization. Bifurcation analysis is calculated to predict and confirm the occurrence of synchronization between two neural circuits. It is found that synchronization can be stabilized between two FHN neural circuits by selecting appropriate values for parameters in the Josephson junction involved in the coupling channel. It gives useful guidance for implementing artificial synapse for signal processing in neural circuits. neuron, synchronization, hybrid synapse, neural circuit, bifurcation Citation:
Zhang Y, Wang C N, Tang J, et al. Phase coupling synchronization of FHN neurons connected by a Josephson junction. Sci China Tech Sci, 2020, 63, https://doi.org/10.1007/s11431-019-1547-5
1 Introduction Biological neurons [1–5] can present a variety of firing patterns and show distinct mode transition in oscillation by changing the intrinsic bifurcation and external forcing current, which can adjust the excitability of the media completely. For example, Wang and Liu [4] proposed a neural circuit for estimating the electrical activities in cerebellar cortex. The involvement and application of patch clamp enables exact detection and analysis on the sampled time series for membrane potential. For extensive nonlinear analysis and prediction, many neuron models [6–10] have been proposed to reproduce the main dynamical properties of *Corresponding author (email: [email protected]; [email protected])
biological neurons by referring to the experimental data. Biological neurons are elastic and the membrance capacitance can be changed when the shape of the neurons is disturbed, as a result,
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