Turing structure during embryogenesis

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 evolved, has been shown to be globally asymptotically stable by using a suitable Liapunov's function.