Two rate equation for

Here also, the Laplace transform method is particularly useful [130]. First, the two rate equations for v1 and vu are linearized and subsequently written in the Laplace domain. 

The theorem allows decomposition of the evolution equation for the second-order tensor into two rate equations for the eigenvalues and eigenvectors of ay, respectively. Then one modifies the equation for the eigenvalues, and keeps the equation for the eigenvectors unchanged. Finally, a new equation is formed by reassembling the equations. This approach preserves objectivity of the equation. For details about objectivity, see for example Tanner (2000). The resulting RSC equation is... 

So, one way to design a chemical oscillator might be to look for systems that obey rate equations like eqs. (4.1). Let us ignore, for the moment, the question of where one might hope to find real systems that have the right kinetics and look first at a beautifully simple model that captures the essence of eqs. (4.1) and points us toward a way of designing real chemical oscillators. The model, proposed by Boissonade and De Kepper (1980), consists of two rate equations for the species x and y ... 

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