Turing (1952) demonstrated that spatially heterogeneous patterns could be formed out of a completely homogeneous field, in which two kinds of diffusible molecules react with each other and engage in random diffusion. A series of studies on reaction-diffusion systems of Turing type, have been developed to explain many examples of pattern formation in chemical reactions and developments.
When the calculation is started from an equilibrium value with small fluctuations, it is known that one of the three types of Turing patterns (spot, stripe and reversal spot patterns) emerges. In this talk, I will consider the parameter conditions to emerge each pattern (spot, stripe or reversal spot pattern).