Localized Pattern in Networks with Lengyel-Epstein Kinetics

2 Localized Pattern in Networks with Lengyel-Epstein Kinetics 

Plots of the concentrations of the inhibitor show the same qualitative behavior. 13.4.2.1 Star Graph 

The simplest case of a network with a complete node is a star graph. We start our exploration of the nonlinear dynamical behavior of Lengyel-Epstein networks with a 10-node star graph, namely of Fig. 13.3a. Theorem 13.17 implies that F = 1, 10. Choosing r = = 1, we expect from (13.125) that a coupling strength 

The resulting activator concentrations are shown in Fig. 13.4, from left to right, top to bottom. In all cases, the patterns are characterized by three constants, p ,  

As a second example of the nonlinear dynamics of Lengyel-Epstein networks, we consider the graph Qi, in Fig. 13.3b. As discussed above, this graph has three completely connected subgraphs, gI i, 2 b,3- Por Gb,iy Theorem 13.14 and 

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