Unilateral regulation breaks regularity of Turing patterns.

摘要: We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. investigate its influence on the character of resulting patterns. The nonsmooth positively homogeneous term τv^{-} has favorable properties, but standard linear stability analysis cannot be performed. illustrate importance nonsmoothness numerical case study, which shows that can considerably change if we replace this arbitrarily precise smooth approximation. However, all approximations yield qualitatively similar patterns although not necessarily developing from small disturbances spatially steady state. Further, show breaks approximate symmetry regularity classical yields asymmetric irregular Moreover, given with produces spatial even for diffusion parameters ratios closer to 1 than same without any