Instabilities in Diffusively Coupled Reactor Networks

We use the results of the previous section to analyze the stability of the uniform steady state of homogeneous arrays of diffusively coupled reactors, whose internal dynamics can be described by the concentration of two species U and V  

As above, the kinetic rate functions Fj and F2 depend on a set of parameters. We display only one explicitly, namely the bifurcation parameter p.. The steady state (Pu Pv) of an isolated reactor is given by 

The homogeneous network of reactors (13.31) has a uniform steady state (USS)  

According to the results of the previom section, the stability of the USS is determined by the eigenvalues of the matrix J(r), 

Tbe second possibility, a stationary spatial or Turing instability, requires that det J(r) = 0, 

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