By Ilya Prigogine, Stuart A. Rice

The *Advances in Chemical Physics* sequence presents the chemical physics and actual chemistry fields with a discussion board for severe, authoritative reviews of advances in each sector of the self-discipline. jam-packed with state-of-the-art examine pronounced in a cohesive demeanour no longer stumbled on in other places within the literature, each one quantity of the *Advances in Chemical Physics* sequence serves because the excellent complement to any complex graduate type dedicated to the research of chemical physics.

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19). Hence each of the polynomials on the right-hand side is a linear combination of the factors (xi - l), for i = 1, . . , tt. Hence each term of these polynomials is divisible by one of the factors (xi - l), for i = 1, . . , n. 7. 5. If x, y and I are the dimensionless concentrations, (diag E h p ( x'ln x) = ( j 2 y ,j l x u , (j l + j 2 ) x , j 2 x 2 ,(jl+j2)z)' and the nonlinear equations are obtained by mutliplying on the left by _v. We write the 36 B. L. CLARKE equations so that every term contains a factor of ( x Y 5;- = -jlJ+ - I), ( y - I), or (I - 1) to get - 1) - ( j , +j2)(y - 1) + ( j l + j 2 ) ( z - 1) i - = 2(j, +j&X - 1) hz - (I - I)] In factorizing, we divided each polynomial by x - 1 to obtain a quotient and a remainder.

The existence of multiple steady states for this j means that these equations have other solutions, which we call a’(j),a”(j), . . If the solution a’@ corresponds to the steady state (h’,j’),whose concentration at steady state is Xi”= hi-’, the dimensionless concentration at steady state is therefore h / h and this is a’@. 51) using x = a’(i). Hence for j = 1, . . 57) 37 STABILITY OF COMPLEX REACTION NETWORKS If this sytem of equations is solved for j' as a function of j, the solution will be unique only if II, is a simplex because the redundant parameters have been used.

Physical Limitations to the Accessible States Molecules occupy a nonzero volume; hence one mole of particles of type i cannot be packed into a less than h,? (say) liters. Thus hi > h,? 58) is a physical constraint equivalent to an upper limit on the solubility of X i . On the average, molecules in a dense medium at room temperature cannot collide more frequently than lOI4 times per second. 59) The part of parameter space satisfying two such restrictions for arbitrary ho E R and jo E R :-d is the potentially accessible region corresponding to ho and jo.