Nonlinear dynamics, oscillatory catalytic reactions

Nonlinear dynamics, oscillatory catalytic reactions, 37 232-236 Norbomadiene... 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

The occurrence of kinetic instabilities as well as oscillatory and even chaotic temporal behavior of a catalytic reaction under steady-state flow conditions can be traced back to the nonlinear character of the differential equations describing the kinetics coupled to transport processes (diffusion and heat conductance). Studies with single crystal surfaces revealed the formation of a large wealth of concentration patterns of the adsorbates on mesoscopic (say pm) length scales which can be studied experimentally by suitable tools and theoretically within the framework of nonlinear dynamics. [31]... 

Chapter 3 is an overview of chemical and biological nonlinear dynamics. The kinetics of several types of reactions -first order, binary, catalytic, oscillatory, etc - and of ecological interactions -predation, competition, birth and death, etc - is described, nearly always within the framework of differential equations. The aim of this Chapter is to show that, despite the great variety of mechanisms and processes occurring, a few mathematical structures appear recurrently, and archetypical simplified models can be analyzed to understand whole classes of chemical or biological phenomena. The presence of very different timescales and the associated methodology of adiabatic elimination is instrumental in recognizing that. 

The proposed model is based on the liquid-phase reactions the rates of escape of volatile species and gaseous O2 and I2 from the system are not considered. There is no direct autocatalytic or autoinhibition step of the form A -hxB (x + 1)B. The feedback is an intrinsic part of the model as a result of mutual combinations between reactions. Moreover, this model has all characteristics necessary to explain the considered catalytic hydrogen peroxide decomposition as one complex nonlinear process having a region of multistability wherein the different dynamic states from simple oscillatory to complex ones and chaos are found. 

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See also in sourсe #XX -- [ , , , ]

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