Abstract
A non-linear reaction-diffusion model of the epigenetic system involving the synthesis and simultaneous intercellular self and cross-diffusion of the activator and inhibitor during embryogenesis has been proposed. It has been observed that the system spontaneously emerges into a stationary dissipative (Turing) structure only in the presence of positive cross-diffusion. That the stationary structure, thus envolved, has been shown to be globally asymptotically stable by using a suitable Liapunov's function.
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