| Abstract: |
| A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called effective equation including the reduced integral kernel (called effective kernel ) in the convolution type. In this talk, we will explain the procedure for the derivation of the effective kernel, and subsequently show that the Mexican hat shaped kernel can be derived from the typical activator-inhibitor systems. Finally, applying our method to other networks of signaling systems, we will investigate how patterns are generated from the derived effective equations in the numerical simulations. |
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