TURING STRUCTURE DURING EMBRYOGENESIS

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