The Lotka Problem Chemical Oscillations

We have just seen that positive feedback can lead to explosive reaction, either by unchecked heating or unchecked population growth. We now consider a different example of instability. Consider the hypothetical mechanism 

Before analyzing this mechanism consider the related problem, where reverse reaction is possible. 

For simplicity assume that [A] has a constant value Aq which may be arranged if, initially, A is in great excess or if the system is open and A is 

Boudart (Princeton, N. J. Princeton University Press, 1958), Vol. 2, p. 196 J. Nicholas, Chemical Kinetics (New York Halstead, 1976), p. 148. 

If there are small perturbations about the equilibrium state the system, as discussed in Section 4.9, relaxes to equilibrium (see Problem 7.4). The displacement variables [X] — Zq, etc., are linear combinations of decaying exponential functions. Direct negative feedback, due to reverse reactions like 2X X + A, keep [X] and [Y] under control no matter what the initial conditions. 

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