JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 13-23.doi: 10.6040/j.issn.1671-9352.0.2022.319

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Global dynamics analysis of a class of Filippov-type HR neuron model

Wenyan LIU(),Shuai QIAO,Chenghua GAO*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-05-30 Online:2023-10-20 Published:2023-10-17
  • Contact: Chenghua GAO E-mail:1299427689@qq.com;gaokuguo@163.com

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Abstract:

Based on the HR neuron model under electromagnetic radiation, a non-smooth control strategy is proposed, in which the membrane potential is utilized as the threshold to determine the switching function corresponding to the electromagnetic induction intensity and external stimulus current. Consequently, a four-dimensional Filippov-type HR neuron model is established. Firstly, the existence, stability, and global bifurcation behaviors of equilibrium points of two subsystems are discussed by using stability theory and numerical simulation. Then, the bistable behavior and evolution modes of subsystems are investigated based on the two-parameter bifurcation analysis. Further, the existence of various equilibrium points and sliding mode dynamics of the system is analyzed by Filippov convex combination method and Utkin's equivalent control method. Finally, the sliding firing modes and bistable features under threshold control strategy are revealed by the method of fast-slow variable dissection.

Key words: Filippov-type HR neuron, threshold control strategy, sliding mode dynamics, bistability, fast-slow variable dissection

CLC Number: 

  • O193

Fig.1

Global dynamic responses of subsystem S1 on the Imax∈[0, 5.5], kmax∈[-2, 3.5] plane"

Fig.2

Global basins of attraction of subsystem S1 for kmax=-0.5, 0, 0.5 on the I×x(0) plane"

Fig.3

Sliding dynamic responses of the system (3) when Imax=1.75, gmax=0.5, Imin=0.98, gmin=-0.5"

Fig.4

Sliding dynamic responses of the system (3) when Imax=1.75, gmax=0.5, Imin=0.98, gmin=-0.5"

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