Relaxation times near ignition and extinction points

Relaxation times near ignition and extinction points 

When the residence time is varied so that we approach an ignition or extinction point in the stationary-state locus, then the flow and reaction curves L and R become tangential. The condition for tangency is R = L and 8R/da = SL/da. Thus the difference between the slopes of R and L decreases to zero. From eqn (8.17) we see that the tangency condition also causes the value of the eigenvalue A to tend to zero. An alternative interpretation, in 

The equivalence between a vanishing eigenvalue and a turning point in the stationary-state locus can be made firmer using the ideas of the singularity theory introduced in the previous chapter. The stationary-state condition, in general terms, for eqn (8.14) is 

Comparing this with eqn (7.41), we can see that here / plays the role of the function F, and that ass is equivalent to x. The condition for a turning point, eqn (7.50), then becomes 

Equation (8.13) gives the appropriate form for l/treiax( = — X) for the cubic autocatalysis model with no inflow of autocatalyst. The condition for the turning point in the stationary-state locus (there is only one) is = 4. 

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