The structure of the functional graph is studied for a discrete dynamic system consisting of two circulants G
,
with different orientations and functionings and with the corresponding vertices being conjugate. The recurrent relation for the number of fixed points is obtained, and the asymptotic behaviour of this number is described. In the case k = 2 the theorems characterizing structural properties, fixed points, pendant vertices and cycles of length 2 of the functional graphs are proved. In particular, the explicit formulas for the number of fixed points and pendant vertices are found.
Download file
Counter downloads: 437
- Title The discrete dynamic system on a double circulant with different functions at the vertices
- Headline The discrete dynamic system on a double circulant with different functions at the vertices
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 6 (Приложение)
- Date:
- DOI
Keywords
генная сеть, дискретная модель, регуляторный контур, циркулянт, функциональный граф, циклы, неподвижные точки, висячие вершины, gene network, discrete model, regulatory loop, circulant, functional graph, cycles, fixed points, pendant verticesAuthors
References
Григоренко Е. Д., Евдокимов А. А., Лихошвай В. А., Лобарева И. А. Неподвижные точки и циклы автоматных отображений, моделирующих функционирование генных сетей // Вестник Томского государственного университета. Приложение. 2005. №14. С. 206-212.
Evdokimov A. A. and Kutumova E. O. The discrete model of the gene networks regulatory loops with the threshold functions // Proc. 7th Int. Conf. on bioinformatics of genom regulation and structure. Novosibirsk, June 20-27, 2010. P. 155.
Харари Ф. Теория графов М.: Наука, 2003.
The discrete dynamic system on a double circulant with different functions at the vertices | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 6 (Приложение).
Download full-text version
Download fileCounter downloads: 1887