Theoretical Study On The Effect Of Fluctuation And Its Control In Complex Chemical Systems

Recently,with the object of the chemical research embed to the complex systems, such as the life system,the surface catalytic system,the nonlinear chemical problem of complex system attracts many attentions.Many processes of the complex systems are nonlinear process,and often showing abundant nonlinear dynamic behavior.In addition,these systems have a high degree of complexity,inevitably affected by a disorder such as environmental fluctuation,internal fluctuation,and spatial randomness,etc.,and the chemical reaction of the systems occurred in all the micro to macro scale,hence they have complex "size effect".But at present,theoretical studies of the nonlinear chemical phenomena for the complex system rarely take into account these complex factors.Therefore,study of the character,mechanism and regulation of various nonlinear dynamics behavior in these systems,especially for the research of the complexity and the interaction between nonlinear dynamics of these systems,have important realistic significance and scientific value.We choose the surface system and the cell system for the study in this dissertation,and investigate the influence of the fluctuation for the oscillation and coherent behavior of the system;as well as the regulative effect of fluctuation correlation in the nonlinear chemical system.The noise would play constructive roles in certain circumstances.Stochastic resonance is the most famous example,and it refers to the response of,the system may reach maximal order at an optimal noise level.There are still many other example like molecular motor,noise induced phase transition,coherent resonance etc..SR still has extending form,the System- Size Resonance.Such effect may connect with signal process in life system,characteristic of nano-catalyzer,and so on.The investigation of these problems is of great importance in understanding meso-seopic dynamics and statistics and discovering life essences on cellular and sub-cellular levels.In the first chapter of dissertation,we introduce the basic theory of nonlinear chemical dynamics and the background involved in this dissertation.Besides the deterministic dynamics method,we have emphasized the theory of mesoscopic stochastic process.On basis of nonlinear dynamic theory,and make use of stochastic normal form and stochastic average method,we make clear the effect of internal noise in mesoscopic chemical systems near Hopf bifurcation theoretically.In this dissertation,we extend this method to the actual complex chemical systems. We study the dynamics of CO+O₂ on Pt surface in the second chapter. Heterogeneous surface catalytic reactions involve various processes such as adsorption,desorption,heat transduction,phase transition and reaction etc.which lead to intricate dynamical behaviors.We investigate the influence of internal noise on the reaction oscillation theoretically,and discovered "the optimal system size",which proved by simulation.Besides 'internal noise','external noise' is also inevitable in actual systems.It is found that there is a competition mechanism between internal and external noise,which contribute in a 'weighted-additive' way to a well-defined effective noise that lead to coherent resonance.The theoretical analysis is based on the stochastic normal form theory proposed in the first part,and reproduced by simulation. The analysis shed some new light on the important role of noise in mesoscopic chemical oscillation systems,and may open perspectives in futher studies.The cell system is investigated in the third part.As one of the most important second messagers in the living cells,cytosolic calcium play a vital role for realize of physiological action,and especially,the calcium system have abundant dynamic behaviors.We mainly investigate the effect of internal noise for calcium signal process,and find out "system size bi-resonance".This phenomenon is related to the dynamics character of the system -canard explosion,and noise could induce semi-harmonic oscillation or relaxation oscillation of reaction rate according to noise intensity.Furthermore,it is also find that the internal noise can enhance the ability of the system to detection of external weak signals,and we disclose a new mechanism of the cell system to feel the external stimuli.Finally,we investigate the regualteing mechanism of fluctuation for the dynamics behacior of Brusselator system.In the real systems,"colored noise" is more realistic to describe the actual fluctuation.We study the diversity of the dynamic behavior for the system affected by different kinds of colored noise,both theoretically and numerically simulated.Moreover,by reinjected noise after a constant time recycling, we put forward a new method for use noise to control nonlinear systems,and point out that one may deliberately control the output motion by adjusting the delay time and the fraction of the secondary part.Since oscillation and noise are of ubiquitous important in many actual systems,our study may find many applications.