Behavior of solutions to an activator-inhibitor system with basic production terms

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We consider an activator-inhibitor system proposed by A. Gierer and H. Meinhardt in 1972, which is a model of the transplantation experiment on hydra. Nontrivial spatial patterns of the activator are expected to emerge in the system, and it is postulated that a change in cells or tissues takes place in the region where the activator concentration is high. But the activator concentration may fail to form spatial patterns if the system does not have a positive basic production term for the activator. We study this phenomenon to understand a role of the basic production terms in pattern formation.


  • MI lecture note series

    MI lecture note series (14), 49-59

    Faculty of Mathematics, Kyushu University


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