Valeriya Tafintseva, Arcady Ponosov
Abstract:
We study piecewise-linear delay differential systems which describe
gene regulatory networks with Boolean interactions.
Under very general assumptions put on the regulatory functions
it is shown how to construct the limit dynamics of the systems by
applying singular perturbation analysis.
The obtained results are compared with those based on the multilinear
representation of the regulatory functions usually considered in the
literature. It is shown that sliding modes may be quite different
in the multilinear and general case.
Polynomial representations of the systems are proposed to describe
generic cases of the dynamics. The results presented in this paper
may give the insight into the theory of gene regulatory networks.
Submitted November 14, 2012. Published January 27, 2013.
Math Subject Classifications: 34K07, 34K26, 34K60.
Key Words: Delay differential equations; singular perturbation analysis;
polynomial representation; gene regulatory networks.
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Valeriya Tafintseva CIGENE - Center for Integrative Genetics at UMB Department of Mathematical Sciences and Technology Norwegian University of Life Sciences (UMB) P.O. Box 5003, Drobakveien 31, As, N-1432, Norway email: valeta@umb.no, tel.: +4796851337; fax: +4764965401 |
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Arcady Ponosov CIGENE - Center for Integrative Genetics at UMB Department of Mathematical Sciences and Technology Norwegian University of Life Sciences (UMB) P.O. Box 5003, Drobakveien 31, As, N-1432, Norway email: arkadi@umb.no |
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