Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 104, pp. 1-36.
A general framework for stability analysis of gene regulatory
networks with delay
Irina Shlykova, Arcady Ponosov,
Yury Nepomnyashchikh, Andrei Shindiapin
Abstract:
A method to study asymptotic properties of solutions to systems of
differential equations with distributed time-delays and Boolean-type
nonlinearities (step functions) is offered. Such systems arise in
many applications, but this paper deals with specific examples of
such systems coming from genetic regulatory networks. A challenge is
to analyze stable stationary points which belong to the
discontinuity set of the system (thresholds). The paper describes an
algorithm of localizing stationary points in the presence of delays
as well as stability analysis around such points. The basic
technical tool consists in replacing step functions by special
smooth functions ("the tempered nonlinearities") and investigating
the systems thus obtained.
Submitted May 20, 2008. Published August 6, 2008.
Math Subject Classifications: 34K60, 92D10.
Key Words: Gene regulation; delay equations; stability.
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Irina Shlykova
CIGENE - Centre for Integrative Genetics,
Department of Mathematical Sciences and Technology
Norwegian University of Life Sciences, N-1430 As, Norway
email: irinsh@umb.no |
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Arcady Ponosov
CIGENE - Centre for Integrative Genetics
Department of Mathematical Sciences and Technology
Norwegian University of Life Sciences, N-1430 As, Norway
email: arkadi@umb.no |
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Yury Nepomnyashchikh
CIGENE - Centre for Integrative Genetics
Department of Mathematics and Informatics
Eduardo Mondlane University, C.P. 257 Maputo, Mozambique
email: yuvn2@yandex.ru |
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Andrei Shindiapin
CIGENE - Centre for Integrative Genetics
Department of Mathematics and Informatics
Eduardo Mondlane University C.P. 257 Maputo Mozambique
email: andrei.olga@tvcabo.co.mz |
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