A model mechanism proposed by Murray [Phil. Trans. Roy. Soc. London B, 295 (1981}, pp. 473-496] for generating wing patterns and eyespots on butterflies and moths is based on a morphogen (S) activated biological switch for a gene product (g). We analyse one of the resulting partial differential equation systems, namely where D, k, k., k2, gc > kz and a are positive constants. We determine analytically the size of the spatial domain where g-+ gc as t-+ oo after an influx of S at the origin. This

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... gives the size of the eyes pot in terms of the mechanism parameters. The analytical problem is a nontrivial singular perturbation expansion which we discuss in detail.