Before revision:  Specific properties of these patterns , such as local phase synchronization, can be predicted from the parameters of the reaction and of the Mexican Hat coupling . When the damping parameters of the reaction and diffusion parts are small and balanced, phase synchronization vanishes but amplitude patterns persist. These results extend our knowledge of the behaviour of coupled neural field equations and its dependence on stochastic fluctuations .
After revision:  Specific properties of these patterns , such as local phase synchronization, can be predicted from the parameters of the reaction and of the Mexican Hat coupling .