Stability Analysis of Photochemically Coupled Reactors

A network of n photochemically coupled reactors is described by the following system of ordinary differential equations  

Here o/2 is a reference level of illumination, the constant illumination experienced by a homogeneous state. The function H(z) has the following properties (i) H is monotonically increasing, (ii) H —oo) = —1, //(O) = 0, H +oo) = 1, and h (0) = 1. a specific example is H(z) = tanh(z), which is used in the numerical simulation described below. The constant k is the coupling strength and L is the Laplacian matrix of the network Q. If the coupling occurs only via the activator, c = 0, if only via the inhibitor, c = 0. The nature of the coupling, inhibitory or activatory, is characterized by the values 1 for c or c . 

As is clear from the structure of (13.169), the stability of the uniform steady state of a photochemically coupled network can be determined by stmctural mode analysis, as in the case of homogeneous diffusively coupled networks. According to Theorem 13.8, X is an eigenvalue of Jg if and only if A. is an eigenvalue of 

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