TY - GEN
T1 - Stability analysis of a dynamical model representing gene regulatory networks
AU - Ahsen, Mehmet Eren
AU - Özbay, Hitay
AU - Niculescu, Silviu Iulian
N1 - Funding Information:
⋆This work is supported in part by the French-Turkish PIA Bosphorus (TUBITAK Grant No. 109E127 and EGIDE Project No. 22974WJ), and by DPT-HAMIT project.
PY - 2012
Y1 - 2012
N2 - In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function.
AB - In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function.
KW - Asymptotic stability
KW - Gene regulatory networks
KW - Hill functions
KW - Nonlinear time delay networks
KW - Schwarzian derivatives
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U2 - 10.3182/20120622-3-US-4021.00020
DO - 10.3182/20120622-3-US-4021.00020
M3 - Conference contribution
AN - SCOPUS:84866100196
SN - 9783902823045
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 191
EP - 196
BT - Book of Abstracts - 10th IFAC Workshop on Time Delay Systems, TDS-2012
PB - IFAC Secretariat
T2 - 10th IFAC Workshop on Time Delay Systems, TDS-2012
Y2 - 22 June 2012 through 24 June 2012
ER -