%Aigaion2 BibTeX export from Bibliography database
%Tuesday 26 May 2026 02:52:41 PM

@MISC{,
            author = {Vejchodsk{\'{y}}, Tom{\'{a}}{\v s} and Jaro{\v s}, Filip and Ku{\v c}era, Milan and Ryb{\'{a}}ř, Vojtěch},
             title = {Unilateral regulation breaks regularity of turing patterns},
              year = {2015},
          abstract = {We consider a classical reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth positively homogeneous unilateral term τv− has favourable properties in spite of the fact that the standard linear stability analysis cannot be performed. We illustrate the importance of the nonsmoothness by a numerical case study, which shows that the Turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation. However, the nonsmooth unilateral term and all its approximations yield qualitatively same patterns although not necessarily developing from arbitrarily small disturbances of the spatially homogeneous steady state. Further, we show that inserting the unilateral source into a classical system breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns. Moreover, a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term. Biologically, these findings can contribute to the understanding of symmetry breaking during morphogenesis.},
  Preprint project = {NCMM},
     Preprint year = {2015},
   Preprint number = {01},
       Preprint ID = {NCMM/2015/01},
http://ncmm.karlin.mff.cuni.cz/db/publications/commit#
}