| Neurons are one of the basic structural and functional units of the nervous system.Computational neurology is a subject which uses nonlinear methods and computer simulation to simulate and study the nervous system at different levels.It is one of the international frontiers of neurophysiology.The cooperation of neuronal cells is inevitably affected by the chemical,biological and physical environment around the neuronal cells.Studying these effects has important implications for the problem of signal detection,propagation,and energy coding in neuronal systems.In this paper,the effects of stimulus signal,noise,electromagnetic induction,coupling,network structure and external electric field are respectively considered to study the vibration resonance and energy coding in single neuron,chaotic resonance and inverse stochastic resonance in neural network motifs,signal transmission in feed-forward neural network,etc.The main results obtained from the researches of this dissertation are summarized as follows:(1)A five layer feed-forward neural network composed of 1000 Hybrid neurons is constructed under electromagnetic induction to study the effects of Gaussian white noise,synaptic weight and inter-layer connection probability on the propagation of subthreshold excitatory postsynaptic current.The propagation efficiency and fidelity of weak signal are studied by calculating the post-spike time histogram,power norm and spiking time precision.It is found that there exists moderate noise intensity which can make the neural signal coding best,the signal transmission fidelity highest,and distinguish weak signal from excitement caused by noise.As a function of connectivity probability,power norm and spike time precision fluctuate with the increasing of inter-layer connectivity probability,and multi-periodic bursting can be detected in both the transmission and output layers.(2)Chaotic resonance and inverse stochastic resonance of triple-neuron feed-forward loop Izhikevich neural network motifs are studied under electromagnetic induction.The chaotic current generated by Lorentz system is input into the feed-forward loop network motifs and Fourier coefficient is calculated.Besides,the bistable Izhikevich neural model and the triple-neuron FFL neural network motifs under electromagnetic induction are constructed to study the inverse stochastic resonance phenomenon caused by electrical autapse and non-Gaussian color noise.The results show that the Izhikevich neuron and its network motifs exhibit chaotic resonance phenomenon with increasing the chaotic current intensity.Electromagnetic induction can enhance the ability of Izhikevich neuron to detect weak signals.The adjustment of parameters of electromagnetic induction makes T2-FFL display more obvious chaotic resonance than T1-FFL,which is different from the influence of system parameter on chaotic resonance.The chaotic resonance effect is robust and is quasi-periodic.Furthermore,it is found that there is a minimum value in the average firing rate curve,which is an inverse stochastic resonance phenomenon.Further research shows that the inverse resonance induced by electrical autapse appears multiple minima with time delay,which is called multiple inverse stochastic resonance.The electromagnetic induction feedback gain coefficient should not be too large under certain conditions,otherwise the network motifs may lose its function to inhibit firing activity.(3)The energy dependence of neuron firing modes and multiple vibrational resonance are studied in Fitzhugh-Nagumo and Hindmarsh-Rose neuron models under the effects of electromagnetic field.Membrane potential and Hamilton energy of Fitzhugh-Nagumo neuron are studied with the variation of high-low frequency current and electromagnetic induction based on Helmholtz theorem.In addition,the vibrational resonance in Hindmarsh-Rose neural model and its coupled system are studied under electric field.The results show that the firing activity of Fitzhugh-Nagumo neuron experiences quiescent,spiking,bursting and even chaotic firing states by changing the parameters such as stimulus intensity,amplitude and angular frequency of high-low frequency signals.The process of discharge activity is accompanied by the storage and release of energy.And it is found that multiple vibrational resonance can be observed in Hindmarsh-Rose neural model whether electric field is considered or not,and electric field weakens the multiple vibrational resonance.The occurrence of multiple vibrational resonance can also be detected in case of bidirectional coupling between two Hindmarsh-Rose neurons,but electric field enhances the multiple vibrational resonance. |
