Stochastic Dynamic Behavior Of Neurons Induced By Electromagnetic Field Driven By Phase Noise

In this thesis,a two-dimensional Fitzhugh-Nagumo（FHN）neuron model is used as the research object.Without the external periodic force,a memory is used to simulate the electromagnetic field environment in which the neuron is located.The parameters of the phase noise are used as the main changing factors,and the parameters of the memory are used as the secondary changing factors.The system exhibits rich coherent resonance behavior driven by the phase noise.When the system is subjected to external periodic forces,the memory is used to simulate the electromagnetic field environment in which the neurons are located.The parameters of the phase noise and the memory are taken as the main changing factors,and the parameters of the periodic signal are taken as the secondary changing factors.The stochastic resonance behavior of a neuron system in a planar region with two-parameter variation is analyzed,and some valuable variation rules are found.Based on the image restoration model of FHN array neuron stochastic resonance,the noisy color digital image is processed and different array sizes are taken.It is found that the larger the neuron array is,the better the noisy image restoration effect is.The main research contents of this thesis are as follows:Firstly,the coherent resonance behavior of FHN neurons induced by electromagnetic fields driven by phase noise is studied.Using the amplitude,period,and noise intensity of phase noise as the main variation parameters,and the parameter variation of memristors as auxiliary conditions,the dynamic analysis of the coherent resonance behavior of FHN neuron systems with dual parameter variations was conducted from three perspectives:the amplitude and period of phase noise,the amplitude and noise intensity of phase noise,and the noise intensity and period of phase noise.In the variation region of these parameter combinations,the system exhibits coherent single,double,and multiple resonance behavior.In particular,under the action of the electromagnetic field generated by the memristor,the system exhibits the optimal coherent multiple resonance phenomenon as the amplitude and period of the phase noise change.In the region where the coherent resonance occurs,the system exhibits a discharge rhythm in which the periodic peak discharge transitions to the periodic cluster discharge.Secondly,the electromagnetic field induced stochastic resonance behavior of FHN neurons driven by phase noise is studied.The memristor was used to simulate the electromagnetic field environment of the nervous system,and the rich stochastic resonance behavior of the FHN neural system driven by phase noise was analyzed.On the one hand,with the amplitude,period and intensity of phase noise as the main change parameters,and the changes of memristor parameters and external periodic signals as the auxiliary conditions,the two-parameter changes were made from the three angles of the amplitude and period of phase noise,the amplitude and intensity of phase noise,and the intensity and period of phase noise,respectively.The stochastic resonance behavior of FHN neuron system was analyzed.In the two-parameter variation region of amplitude and period of phase noise,when the system has strong resonance with external periodic signal with the increase of period of external periodic signal,the period of phase noise also increases,so does the number of period of system cluster discharge.Especially,when the period of phase noise is almost the same as that of the external periodic signal,the stochastic resonance phenomenon of the system is more obvious.On the other hand,with the parameters of memristor k,₁k andk₂as the main variable parameters,the phase noise parameters and the changes of external periodic signals as the auxiliary conditions,the random dynamic behavior of FHN neural system is analyzed in detail from the perspectives of k and₁k,k andk₂,₁k andk₂.In the parameter plane region of k and₁k,k andk₂,with the gradual increase of the period of the external periodic signal,the resonance behavior of the system shows a relatively similar trend,which gradually evolves from a single formant to two formants and finally to a single formant.In the parameter plane region ofk₁ andk₂,as the period of the external periodic signal increases gradually,the whole system only presents one formant,and different periodic signals have similar influences on the stochastic resonance behavior of the system.Finally,the application of neural stochastic resonance in image restoration.By establishing the array neuron model,the noisy color digital image is processed as the input of the array neuron model,and the image noise is removed based on the FHN array neuron stochastic resonance model,and the noise image is restored.