Effects Of Noise On Nonlinear Systems

Noise is an elemental factor that should be considered in many real nonlinear systems, and it is one of the sources of complex behaviors. In this thesis, the effects of Gaussian noise and non-Gaussian noise on three kinds of nonlinear systems were studied. The effects of cross-correlated noise on the optical bistable system and the single-mode laser system was studied using the stochastic dynamics theory. The stochastic resonance(SR) phenomenon was found for the optical bistable system with cross-correlated Gaussian white and Gaussian colored noise. The relaxation time of the optical bistable system with colored cross-correlated Gaussian colored noise was investigated. The steady state properties of a single-mode laser system was studied. Using the stochastic simulation method, the effects of non-Gaussian noise on a calcium oscillation system was investigated and the phenomenon of coherence resonance (CR) was found. The influence of sub threshold periodic signal and Gaussian colored noise on the calcium oscillations system was investigated, and the multiple stochastic resonance(SR) phenomenon was found. In particular, the following results have been presented in this thesis:For the optical bistable system, the signal-to-noise ratio (SNR) has a peak with increasing white noise intensity or the colored noise intensity, this means the SR phenomenon occurs. The self-correlation time of the colored noise can induce the general stochastic resonance phenomenon, and the larger cross-correlation intensity, the more obvious the SR phenomenon is. The effects of colored cross-correlated Gaussian colored noise on the relaxation time of the system in the steady state was studied. The larger cross-correlation time of the two noise or the self-correlation time of the multiplicative colored noise can delay the system fluctuation decay. However, the larger cross-correlation intensity or the multiplicative noise intensity can accelerate the system fluctuation decay. The relaxation time of the system in steady state decreases with increasing additive noise self-correlation time, and increases with increasing additive noise intensity. The effects of non-Gaussian and Gaussian white noise on the correlation function of the system was studied, and found the correlation function has a maximum with increasing non-Gaussian noise intensity; the parameter of the non-Gaussian noise can increase or decrease the system fluctuation appearance probability with different cross-correlation intensity between the two noises.The effects of Gaussian white and non-Gaussian noise on the single-mode laser system was investigated, and found the probability density function of the laser intensity has a maximum. The mean laser intensity increases with non-Gaussian noise self-correlation time increasing, and the slope of the mean laser intensity with self-correlation time curve becomes small with increasing self-correlation time. The larger cross-correlation intensity or the non-Gaussian noise parameter, the smaller mean laser intensity is. The larger self-correlation time of the non-Gaussian noise, the smaller laser intensity dispersion is.Using stochastic simulation method, the effects of noise on a calcium oscillation system was studied in three respects.(1)The effects of non-Gaussian noise on a calcium oscillation system was investigated and found non-Gaussian noise can induce oscillation even though the system is in resting-state as no noise in the system. The noise oscillation should be most orderly with suitable noise intensity. The non-Gaussian noise can induce general CR phenomenon as the coherence factor has a maximum with increasing correlation time.(2) The effects of colored noise on the system with weak signal was studied, and the stochastic multiresonance phenomenon was found. The coherence factor has some maximum with increasing signal period, and the larger noise intensity, the fewer maximum number.(3) The effects of colored noise and noise delay on the system was investigated as the system in steady state. The reciprocal coefficient of variance has two maximums with increasing noise intensity, this means the colored noise can induce coherence bi-resonance phenomenon; The reciprocal coefficient of variance has three peaks with increasing self-correlation time of the colored noise; Large value of the injector coefficient reduces noise induced spikes regularity.