Stochastic Resonance And Its Application In Neurodynamic Model

Because of the cooperation between a system, the input noise and input signal of the system, at some mediate noise intensity, the input signal is amplified, thus the output signal-to-noise ratio (SNR) reaches a maximum. This nonlinear phenomenon is called stochastic resonance (SR). Stochastic resonance in a broad sense means the output signal of the system is a non-monotonic function of some parameter of the noise, of the system or parameter of the input signal. Coherence resonance (CR) characterizes a nonlinear phenomenon that a noisy excitable system responds with an excitation sequence called a "spike train", at an optimum noise intensity the spike sequence is much more regular.In this paper, the SR phenomena of some linear and nonlinear systems are investigated. The application of the SR and CR in integral-and-fire model and FitHugh-Nagumo model is researched. The main contributions are listed below:1. The SR in a first-order linear system subject to additive and multiplicative dichotomous-noise (DN) is investigated. By using the properties of the DN and linear-response theory, the expressions have been found for the output SNR of the system. It is shown that the SNR is a non-monotonic function of the correlation time of the additive and multiplicative DN, and it varies non-monotonously with the intensity of the multiplicative DN as well as with the external field frequency.2. The SR phenomenon of an over-damped second-order linear system subject to the DN is investigated. Result shows that the output amplitude gain (OAG) is a non-monotonic function of the strength, the correlation rate of the DN, as well as the damping coefficient and frequency of the driving signal. In addition, by choosing appropriate parameters of the noise, the OAG of the noisy system can be larger than that of the noise-free system.3. The SR in a bistable system subject to the DN is investigated. It is found that the SNR is a non-monotonic function of the correlation time of the DN, two peaks can occur on the curve of the SNR. The spectral power amplification (SPA) is a non-monotonic function of the strength of the DN. 4. The SR phenomenon of an overdamped Brown particle in an asymmetric bistable potential, driven by external periodical signal and multiplicative noise is investigated. The expressions have been obtained for the quasi-steady-state probability distribution function. It is found that the input energy (IE) pumped into the system by the external driving shows a SR-like behavior as a function of the strength and correlation time of the noise and as a function of the asymmetry potential of the system.5. The CR and the SR phenomenon in the FitzHugh-Nagumo model induced by colored noise are investigated. It is shown that the coefficient of variation (CV) and the SNR are non-monotonic functions of the correlation time of and intensity of the colored noise.6. The CR phenomenon of a linear integral-and-fire model subject to a neurotransmitter Poisson point trains and a voltage-gated noise is investigated. It is shown that the interval-spike-interval (ISI) is a non-monotonic function of the intensity of neurotransmitter arrivals trains and the strength of the voltage-gated channel noise.7. The CR phenomenon of a nonlinear integral-and-fire model subject to a voltage-gated channel noise and a synaptic noise is investigated. It is shown that the probability distribution of the first fire (FPD) and the firing rate (FR) are non-monotonic functions of the strength of the voltage-gated channel noise and the synaptic noise. Furthermore, by choosing appropriate noise parameter, spontaneous fire of neuron can occur.