Dynamic Analysis of Neurons by Josephson Junction

doi:10.19596/j.cnki.1001-246x.8667

Abstract

Abstract:

A four-dimensional neuron model with Josephson junction is constructed by introducing Josephson junction into HR neuron. Firstly, the dissipative property of the system and the stability of the equilibrium point are obtained through theoretical analysis. By adjusting the Josephson junction parameters to observe the bifurcation of the electric-coupled system, it is found that the system shows rich dynamic characteristics such as period-doubling bifurcation and addition-period bifurcation including chaos within the appropriate parameter range. A global coupled neural network is constructed under the action of chemical synapses. Synchronization factors are used to describe the synchronization degree of the system under different parameters. It is found that coupling strength and Josephson junction parameters can affect the discharge synchronization state of the system.

Key words: Josephson junction, coupling, equilibrium point, discharge bifurcation, synchronous

CLC Number:

O193
O441.3

Tongtong XIAO, Xinying LI, Yuqing QIAN. Dynamic Analysis of Neurons by Josephson Junction[J]. Chinese Journal of Computational Physics, 2023, 40(6): 752-760.

Figures/Tables 9

Fig.1 Bifurcation diagrams of the system under different parameters (a) k; (b) χ0(k=0.1); (c) χ0(k=0.2)

Fig.2 Phase diagram to different values of k (a) k=-0.7; (b) k=-0.1; (c) k=0.2

Fig.3 Two-parameter bifurcation diagram (a) g and χ0; (b) r and k; (c) r and χ0

Fig.4 Similar function diagram of coupling strength D in different parameters k (a) k=0.2; (b) k=-0.2

Fig.5 Time history diagram and phase diagram of the system under different coupling strength D at k=0.2 (a) and (d) D=0.1; (b) and (e) D=0.2; (c) and (f) D=0.6

Fig.6 The two-parameter similar function graph of r and χ0 under different coupling strength (a) D=0.5; (b) D=0.2

Fig.7 Synchronization factor plot of different parameters (a) synchronization trend of the system with D; (b) synchronization trend of the system with k

Fig.8 Time history diagram and phase diagram of the system under different k values (a) and (c) k=0.2; (b) and (d) k=0.8

Fig.9 Two-parameter synchronization factor diagram of r and χ0 at different k (a) and (c) k=0.1; (b) and (d) k=0.5

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