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Abstract
Noise exists widely in the nervous system, and plays a crucial role in the nervous system information processing. Noise can not only enhance but also weaken the ability of the nervous system to process information. Neurons are in a complex and variable electromagnetic field. Electromagnetic induction plays an important role in regulating the changes of neuronal membrane potential. Therefore, this paper simulates the electromagnetic field environment of the nervous system with a memristor and analyses the rich coherence resonance behavior of FitzHugh‐Nagumo (FHN) neuron system under the drive of phase noise. By taking the amplitude, period and noise intensity of phase noise as the main parameters and the parameters of memristor as auxiliary parameters, the two‐parameter changes are made from the angle of the amplitude and period of phase noise, the amplitude and intensity of phase noise, and the noise intensity and period of phase noise, respectively. The dynamic behaviors of coherent resonance of FHN neuron system are analyzed from the amplitude and period, amplitude and intensity as well as intensity and period of phase noise, respectively. When the amplitude and period of the phase noise and the intensity and period of the phase noise are used as independent variables for the two‐parameter analysis, the FHN neuron system shows rich dynamic behaviors such as coherence mono‐resonance, coherence bi‐resonance and coherence multi‐resonance. Especially when the amplitude and period of phase noise change as two‐parameter, the system presents a coherence resonance of discharge pattern with period‐adding cluster discharge at the valley. When the amplitude and intensity of phase noise are taken as independent variables for two‐parameter analysis, FHN neuronal system presents single or dual coherence resonance at any value of noise intensity with the change of phase noise amplitude. The simulated results show that the FHN neuron system demonstrates rich coherence resonance behaviors under the drive of phase noise when the effect of electromagnetic induction in the nervous system is simulated by memristor.
Highlights
Noise exists widely in the nervous system, and plays a crucial role in the nervous system information processing
When the amplitude and intensity of phase noise are taken as independent variables for two-parameter analysis, FHN neuronal system presents single or dual coherence resonance at any value of noise intensity with the change of phase noise amplitude. e simulated results show that the FHN neuron system demonstrates rich coherence resonance behaviors under the drive of phase noise when the effect of electromagnetic induction in the nervous system is simulated by memristor
Jia et al studied the counterintuitive phenomenon of inhibitory autosynaptic enhancement of coherence resonance in HH neural networks, which was well explained by the peak of inhibition rebound (Pir). ey introduced the Gaussian white noise into the excitatory coupled HH neuron network, and studied the coherence resonance dynamic behavior of the system was studied in detail on a plane composed of every two parameters such as noise intensity, adaptive intensity and time delay [24]
Summary
To analyze the random dynamic behavior of a non-linear neuronal system under the influence of magnetic flux variation and phase noise, this paper introduces flux-controlled memristor and phase noise into FHN neuron model, and analyzes the coherence resonance behavior of FHN neuron system. e model is established as follows: dx x3 ε x − − y + kρ(φ)x,. To analyze the random dynamic behavior of a non-linear neuronal system under the influence of magnetic flux variation and phase noise, this paper introduces flux-controlled memristor and phase noise into FHN neuron model, and analyzes the coherence resonance behavior of FHN neuron system. Where in kρ(φ)x represents the feedback current of electromagnetic induction on the membrane potential, and regulates the excitability of the cell membrane potential. It is expressed as: i′ dq(φ) dq(φ) dφ dt (5). In (3), D represents the noise intensity of Gaussian white noise ξ(t) which meets the following statistical properties, as shown in (6):. In (4), φ represents the magnetic flux across the membrane, k1x represents the magnetic induction change induced by the membrane potential, and k2φ represents the flux leakage
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