Dynamical Analysis Of The Neuronal FitzHugh-Nagumo Model

Noise is widely considered to be harmful. It affects the system’s regularity and stability. However, more and more studies show that noise signals play a positive role in transmitting and amplifying signals. When noise acts on the nervous system, it will affect the discharge mode of neurons in cortex of brain. By observing the firing pattern of neurons under different conditions, we can analyze the reasons and conditions that the nonlinear dynamic behavior of neurons produce, as well as the relationship between the pulse sequence and neurons by external stimulant.The nonlinear system driven by noise mainly embodies the phenomenon of stochastic resonance and coherence resonance. Many theoretical studies about stochastic resonance and coherence resonance make use of the white noise and colored noise, less bounded noise and non-Gaussian noise. Different noise is input in the FHN model of the excitation system, we explore the action of nonlinear dynamic under bounded noise and random phase and non-Gaussian noise respectively. The specific structure of the full text is as follows:In Chapter 1, first the nonlinear dynamics, neurons, noise and stochastic resonance and coherence resonance are introduced. Secondly, this paper’s researching significance and main content are showed.In Chapter 2, the origin and stability and phase diagram analysis of the neuronal model of FitzHugh-Nagumo are presented.In Chapter 3, we mainly study coherence resonance of the neuronal model of FHN driven by bounded noise. Firstly, we analyze that how the frequency influence the number of output action potentials of FHN neural model under the noise intensity of bounded noise to be zero. Secondly we investigate that the noise intensity and the frequency of bounded noise have the influence of the firing regular pattern of membrane voltage and the coefficient of coherence resonance and the corresponding autocorrelation function.In Chapter 4, we investigate coherence resonance (CR) in the FitzHugh-Nagumo neurons models driven by random phase. We demonstrate numerically that the intensity and correlation of random phase can influence the firing sequence of neuronal membranes. Taking the coefficient of coherence resonance as a ratio, it is concluded that the phenomenon of coherence resonance is produced. Finally, we discuss the synchronization phenomenon of two coupled FHN neural model driven by the random phase.In Chapter 5, we analyze the phenomenon of stochastic resonance of FHN driven by non-Gaussian noise. We demonstrate numerically that the non-Gaussian noise and the periodic signal can induce SR by adjusting the intensity of non-Gaussian noise.In Chapter 6, conclusion and discussion are provided.