| Issue |
ITM Web Conf.
Volume 16, 2018
AMCSE 2017 - International Conference on Applied Mathematics, Computational Science and Systems Engineering
|
|
|---|---|---|
| Article Number | 01005 | |
| Number of page(s) | 3 | |
| Section | Communications-Systems-Signal Processing | |
| DOI | https://doi.org/10.1051/itmconf/20181601005 | |
| Published online | 09 January 2018 | |
On attracting sets in artificial networks: cross activation
Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Rainis boul. 29, Riga, Latvia
Corresponding author: felix@latnet.lv
Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalues corresponding to any of the critical points are negative. An example for a particular choice of sigmoidal function is considered.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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