Nonlinear Analysis And Control Of The B-Z Chemical Oscillating System

The different nonlinear phenomenon in chemical reaction systems has been an extensively investigated topic over the past few decades since the B-Z oscillating reaction was exposed.Many theoretical and experimental results on chemical reaction have been published due to its great application in practical production.With the development of the modern nonlinear analytical methods,which provide effective tools for studying various complex phenomena of nonlinear systems.For the chemical oscillating system or coupling system,when parameters and the initial conditions changed,the complex mechanism is investigated by applying the modern nonlinear analytical methods,and the chaotic control and chaotic synchronization are explored. The main research work of this article has several parts as follows:In the first section,the basic concept,the development history,research results and application of chemical oscillating system are introduced.Finally the selected topic background and the research significance of this paper is given.In chapter 2,the basic concepts of nonlinear dynamics and the analysis methods of nonlinear chemical reaction are introduced,and the concepts related to nonlinear phenomenon are described,such as Spatio-Temporal Series,power spectrum,attractor and poincare section.In chapter 3,the complicated dynamical behavior of autocatalytic chemical reaction of 3-variable CSTR system under time delay feedback is analyzed,and the bifurcation characteristic of reaction process is discussed and compared respectively at different feedback coefficients and delay time.It is pointed out that there exist different chaotic attractors with the increase of feedback coefficients,and the behavior characteristics with different time scales is more obviously,while with the increase of the delay time,chaos attractors can be observed not only via the cascading of period-doubling bifurcation,but also via the instability of quasi-periodic solution.In chapter 4,based on bifurcation characteristics of autocatalytic chemical reaction,the complicated dynamical behaviors of reaction system and coupling system with two typical excitation frequency have been discussed.There are lots of abundant dynamical behaviors in reaction when excitation frequency equal to natural frequency of autonomous system,such as chaos mutation and inverted period doubling bifurcation;However,because of the scale difference between the natural frequency and the excited frequency,the periodic solution directly bifurcates to a quasi-periodic solution and further to special chaos,and obvious fast-slow effect can be observed when chaos immediate instability to periodic solution.For coupling system,there are great changes of the dynamical behaviors undering non-uniform initial conditions via changing coupling strength.In chapter 5,the reaction characteristics of coupling chemical reaction systems both considering time delay or not have been discussed.There are different dynamical behaviors in reaction systems of different conditions,therefore,it is necessary to consider time delay when analyzing coupled system,so as to reflect practical process more accurately.In chapter 6,for autocatalytic chemical reaction,a new reaction system which solution is based on the concentration is designed,and the new model is given.It's obvious that great changes have taken place in dynamical behavior,and there are lots of abundant dynamical behaviors in reaction,such as chaos mutation and inverted period doubling bifurcation.For some bifurcation parameters,fast-slow effect can be observed in reaction system.In chapter 7,the problems of synchronization and lag synchronization for chemical reaction system composed of two CSTRs are proposed.First,a new method is proposed to design the controlling function.The range of the coupling strength to realize the synchronization between two chemical systems is investigated both for the two cases with static velocity as well as periodically disturbed velocity of the input material,then numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.It shows that the method is suitable for both autonomous system and non-autonomous system with periodic perturbation.Then,the problem of lag synchronization for chemical reaction system composed of two CSTRs is proposed.Based on Lyapunov stability theory,the controller which can make reaction reach lag synchronization is obtained by suitable selecting the output and the synchronous signals.Then numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.Finally it is pointed out that there exist two different time scales in error system of lag synchronization.In chapter 8,the control for chemical reaction system composed of two CSTRs is explored.Based on Lyapunov stability theory and anti-synchronization thought,a general scheme is presented which can be used to control the concentration of the whole reaction system in some special states by selecting the controller and the input signal.The scheme has no special requirements to system,and without structuring Lyapunov functions.Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.At last,some meaningful results are summarized in the end of this paper.Also some existing problems as well as the future work are pointed out.