Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

Abstract

An improved Hindmarsh-Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high-low-frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high-low-frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low-frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high-low-frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high-low-frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high-low-frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.

Keywords: bifurcation; bioelectric potentials; diverse high-low-frequency signals; electrical autaptic regulation; electromagnetic radiation; external high-low-frequency stimulus; external periodic signals; high-low-frequency forcing current; high-low-frequency signal; improved Hindmarsh-Rose neuron model; membrane potential; memristors; neural nets; neuronal firing modes; neurophysiology; numerical analysis; periodic high-low-frequency current; research neuronal networks; synchronisation; synchronisation modes; white noise.

Fig. 1

Time series of membrane potential in a neuron under different angular frequency ω: A = B = 1.0, N = 200, g = −0.5, τ = 20 (a) ω = 0.001, (b) ω = 0.03, (c) ω = 0.05, (d) ω = 0.1

Fig. 2

Bifurcation diagram associated with different angular frequency ω: A = 1.0, B = 1.0, N = 200, g = −0.5, τ = 20. ISI denotes the inter‐spike interval in membrane potential series

Fig. 3

Bifurcation diagram associated with amplitude B of the high‐frequency forcing current: A = 1.0, ω = 0.01, N = 200, g = −0.5, τ = 20. ISI denotes the inter‐spike interval in membrane potential series

Fig. 4

Evolution of action potential and energy function with time are calculated by changing the high–low‐frequency forcing current. The forcing current is triggered at t = 1000 time units. For (a1, b1) B  =  1.0, ω  =  0.001, (a2, b2) B  =  0.1, ω  =  0.01

Fig. 5

Distribution of the stable state by high–low‐frequency forcing current: A = 1.0, N = 200, g = −0.5, τ = 20

Fig. 6

Time series of membrane potential in a neuron under different angular frequency ω of high–low‐frequency electromagnetic radiation: A = B = 1.0, N = 200, I_ext = 1.8, g = −0.5, τ = 20 (a) ω = 0.001, (b) ω = 0.01, (c) ω = 0. 3, (d) ω = 0.05

Fig. 7

Bifurcation diagram associated with different angular frequency ω of high–low‐frequency electromagnetic radiation: A = 1.0, B = 1.0, ω = 0.01, N = 200, g = −0.5, τ = 20. ISI denotes the inter‐spike interval in membrane potential series

Fig. 8

Evolution of action potential and energy function with time are calculated by changing the external high–low‐frequency electromagnetic radiation. The electromagnetic radiation is triggered at t = 1000 time units. For (a1, b1) B  =  0.1, ω  =  0.01, (a2, b2) B  =  1.0, ω  =  0.001

Fig. 9

Distribution of the stable state by high–low‐frequency electromagnetic radiation: A = 1.0, N = 200, I_ext = 1.8, g = −0.5, τ = 20

Fig. 10

Time series of membrane potential of neurons under different noise intensity D of white Gaussian noise. The high–low‐frequency forcing current is triggered at t = 1000 time units and the white Gaussian noise is triggered at t = 3000 time units: A = B = 1.0, ω = 0.01, N = 200, g = −0.5, τ = 20 (a) D = 0.1, (b) D = 1.0, (c) D = 5.0, (d) D  = 10.0

Fig. 11

Time series of membrane potential of neurons under different noise intensity D with periodic high–low‐frequency electromagnetic radiation. The high–low‐frequency signal is triggered at t = 1000 time units and the white Gaussian noise is triggered at t = 3000 time units: A = B = 1.0, ω = 0.01, N = 200, I = 1.8, g = −0.5, τ = 20 (a) D = 0.1, (b) D = 1.0, (c) D = 5.0, (d) D = 15.0