Gorban : Invariant Sets ( A
نویسنده
چکیده
Some sets in the space of compositions possessing an invariance property are considered for a closed system, where a complex chemical reaction of a known mechanism proceeds. If the vector of concentrations belongs to such a set at a certain moment of time, it will remain within it at any succeeding moment. Some possible applications are discussed. 3aKpbITOfl CHCTeMM, B KOTOpOl~ npoTeKaeT cHoXCd-Ia~ XNMHtlecKalt peaKllHtl C H3BeCT-HblM MeXaHH3MOM, pacCMaHpHBaIoTc~ MItO>KeCTBa B rrpocTpaacrBe COCTaBOB, o6na~alott~e CBOI~CTBOM I4HBapHaHTHOCTH: ecntt BeKTOp KOHIleHTpaIIHl~ npl4ltagjie~HT TaKoMy MHO-)KeL'TBy B tleKOTOpbIfl MOMENT BpeMeHH, OH 6y~eT ne~KaTl~ B H~M H BO Bce nocne/IyiolLI4e MOMeHTbI. O6cyi~cjIaIOTCg BO3MO)KI~Ie npltflO>KeHIIR. The problem of a priori evaluation of trajectories without taking into consideration the values of rate constants on the basis of the reaction mechanism itself is important when studying the dynamics of complex chemical processes. These evaluations may be obtained by studying invariant subsets of the composition spaces where the trajectories once entering at a certain moment remain inside of it at any succeeding moment. Invariant sets (I. S.) depending only on the reaction mechanism and the location of the point of detailed equilibrium (P. D. E.) are discussed here, Special attention is paid to the I. S. which are minimal among those containing some (arbitrary) point. Consider the system of reactions e p l A1 +" " " + pnAn ~ ~plA1 +" ,. + /~pnAn (1 < p < N) (1) 187
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