Study On The Influence Of Noise On Neural Activity

The noise has been played an important and constructive role on study of nonlinear dynamical, in particular in the neuronal dynamical systems. Biological systems operate in the stochastically evolving environments, the noise can influence the information transmission properties of cortical neurons, the phenomena of the stochastic resonance (SR), coherence resonance (CR) and synchronization have been found. The main result of SR shows that noise at a proper strength optimizes the response of a nonlinear system to a subthreshold periodic signal. An optimal strength of noise can induce the most coherence motion in the system. SR-like behavior of the coherence motion can be induced purely by noise even in the absence of an external signal for system, such as self-sustained oscillations at close to bifurcation point. The phenomenon has been called coherence resonance or autonomous SR. Coherence resonance describes the occurrence of an increased regularity of the response driven by an appropriately chosen amount of noise, in this case no external signal is needed. And the phenomenon of array enhanced stochastic coherence and array enhanced stochastic coherence have been also studied in coupled neuronal systems. Ordinarily the neuronal models are among the most widely used dynamics to study the noise-induced dynamical resonance behavior in theoretical neuroscience, include the much simpler inter-and fire (IF) model, the four-dimensional Hodgkin-Huxley (HH) and two dimensional FitzHugh-Nagumo(FHN) model and so on. All of the models consist of differential equations that are able to reproduce on served neuronal behavior such as excitability refractoriness. When these models are driven by noise, a variety of excitation phenomena including stochastic resonance and coherence resonance has been observed.In this paper, this thesis organized according to the order from single neuron to coupling neuronal network, the phenomena of the noise-induced stochastic resonance (SR), coherence resonance (CR) and the information transmission properties have been studied in neural dynamics systems. The gold of this dissertation is to know the neuron dynamics system can deal with the information effectively at different level under the control of the noise and other parameters of the system. The main works in the paper include three aspect:First, in single neuron model, the phenomenon of coherence resonance in a nonlinear integrate-and-fire neuronal models(NIF) subject to correlated multiplicative synaptic and additive voltage-gated channel noise are investigated. Based on the adiabatic approximation theory and the unified colored approximation method, the analytic expression of the probability distribution of the first fire (FPD) and the coefficient of variation (CV) the inter-spike interval of firing is obtained. It is shown that the FPD and the CV are a function of intensities of the multiplication synaptic colored noise, the additive voltage-gated channel noise white noise, the correlation time of multiplicative noise and the strength of the correlation between noises. By choosing appropriate noise parameter, the phenomenon of coherence resonance can occur. Meanwhile, the effects of intensities of the multiplication synaptic noise, the additive voltage-gated channel noise, the correlation time of multiplicative noise and the strength of the correlation between noises on coherence resonance are discussed. It is found that the SNR is a non-monotonic function of the correlation time, and the SNR show a maximum at appropriate noise level.Second, the phenomenon of coherence resonance (CR) of a leaky neuron model subject to correlated multiplicative synaptic and additive voltage-gated channel noise is investigated. Based on the unified colored approximation theory and Euler schemes, the evolution of the membrane potential and the coefficient of variation (CV) of the interval-spike-interval of the neuron firing have been obtained. It is shown that the CV can be decreased at a certain intensity of noise and the coupling strength without external signal, so that the coherence of the system is maximal, the phenomenon of CR can take place. Meanwhile, the effects of intensities of the multiplication synaptic noise, the additive voltage-gated channel noise, the correlation time of multiplicative noise, the strength of the correlation between noises and the coupling strength on coherence resonance are discussed.Third, the information transmission properties of neural populations in parallel neuron network and the phenomenon of coherence resonance in the myelinated series coupled FitzHugh-Nagumo neuron models driven by the noise is investigated. The nodal membrane size in each node of Ranvier influences the intensity of noise which originated from the turn on of ion channels. Based on the method of forth steps stochastic Runge-Kutta methods, the interval-spike-interval (ISI) of the neuron firing and the coefficient of variation (CV) have been obtained. It is shown that the CV can be decreased at a certain intensity of noise influenced by the nodal membrane size and the coupling strength without external signal in the chemical synapses coupling, so that the coherence of the network is maximal, the phenomenon of CR can take place. The effects of the intensity of noise, the coupling strength and the neuron number on coherence resonance are discussed.