Study On The Effect Of Fluctuation In Mesoscopic Chemical Systems: The Role Of Non-Gaussian And Non-Markovian Behavior

In recent years, theoretical and experimental studies of mesoscopic systems have become the frontier of science development. In mesoscopic scale, the chemical reactions could be described as discrete stochastic processes and the fluctuation is the intrinsic property. The principal of statistic mechanics indicates that the fluctuation in mesoscopic chemical system is so significant that it will affect the dynamics of the system dramatically. By far, study on the effect of fluctuation in mesoscopic systems has become an important issue for statistic mechanics. It is noted that mesoscopic chemical systems exhibit quite different phenomena under the influence of fluctuation due to the complexity of their intrinsic dynamical features. Therefore, study of the character, mechanism and regulation of these complex factors and the interaction between the complex dynamical behaviors and the fluctuation in the system is crucial for getting an insight to the underlying mechanism of the phenomena induced by fluctuation. In this thesis, we have studied the following two kinds of complex dynamical features in mesoscopic systems which are related with fluctuation:The non-Gaussian behaviorFluctuation plays an important role in affecting the non-linear dynamical behaviors of the mesoscopic system. Former works on the effect of fluctuation assume that the fluctuation obeys Gaussian distribution. However, in real physical and chemical systems, the fluctuation constantly exhibits non-Gaussian behavior. The effect of such non-Gaussian fluctuation has drawn great interests in recent years and plenty of interesting features have been uncovered. Nevertheless, the effect of non-Gaussian fluctuation on the oscillation behavior in chemical systems with Hopf bifurcation has not been studied yet. In this thesis, we have investigated the effect of non-Gaussian fluctuation on the noise induced oscillation in the vicinity of Hopf bifurcation. It is found that the non-Gaussian behavior of the fluctuation could induce nontrivial effect on the regularity of the noise induced oscillation. We also found that the correlation time and the distribution of the fluctuation work cooperatively to tune the oscillation behavior. By performing stochastic normal form analysis, we illuminate the underlying mechanism of such phenomenon.The non-Markovian behaviorIn the last decade, with the development of life science, several interesting characters of the structures and functions in living organism have been uncovered. It is demonstrated that the non-Markovian behavior induced by the high degree of complexity during the gene expression process is inevitable in vivo. On one hand, such non-Markovian behavior may interact with the internal fluctuation and trigger many nontrivial dynamical phenomena. On the other hand, the non-Markovian behavior itself could significantly affect the dynamics of mesoscopic chemical systems. In this thesis, we have studied the cooperative effect of internal noise and the non-Markovian behavior in gene regulatory process by using numerical simulation together with stochastic normal form analysis. It is found that internal noise could enhance the robustness of system to non-Markovian behavior and such robustness shows different dependence on the synthetic and degradation rate of the protein. We also study the effect of non-Markovian behavior on the stability of a genetic toggle switch. The results indicate that the non-Markovian behavior could not only affect the stability of the bistable switch, but also the dynamics of the transition process.