TY - GEN
T1 - Robust hyperbolicity of multiple equilibria and analysis of the cellular reprogramming process
AU - Ikuta, Hikaru
AU - Inoue, Masaki
AU - Imura, Jun Ichi
AU - Adachi, Shuichi
N1 - Funding Information:
This research is supported by the Grant-in-Aid for Young Scientists (B), No.26820163 from JSPS
Publisher Copyright:
© 2015 EUCA.
PY - 2015/11/16
Y1 - 2015/11/16
N2 - We propose a hyperbolicity analysis method for multiple equilibria of a nonlinear system with dynamic uncertainties. Since dynamic uncertainties alter the location and even the existence of equilibria, it is difficult to evaluate the hyperbolicity of equilibria for such a system. In this paper, we provide an analysis method to determine whether all equilibria robustly maintain their hyperbolicity under the existence of a norm-bounded class of dynamic uncertainties. The displacement of the equilibria is considered explicitly to evaluate the hyperbolicity. Finally, the proposed method is applied to a genetic network model of induced pluripotent stem cells (iPSCs), to explain how one reprogramming mechanism of iPSCs is robust against various uncertainties. Hyperbolicity of multiple equilibria plays a crucial role in the reprogramming mechanism.
AB - We propose a hyperbolicity analysis method for multiple equilibria of a nonlinear system with dynamic uncertainties. Since dynamic uncertainties alter the location and even the existence of equilibria, it is difficult to evaluate the hyperbolicity of equilibria for such a system. In this paper, we provide an analysis method to determine whether all equilibria robustly maintain their hyperbolicity under the existence of a norm-bounded class of dynamic uncertainties. The displacement of the equilibria is considered explicitly to evaluate the hyperbolicity. Finally, the proposed method is applied to a genetic network model of induced pluripotent stem cells (iPSCs), to explain how one reprogramming mechanism of iPSCs is robust against various uncertainties. Hyperbolicity of multiple equilibria plays a crucial role in the reprogramming mechanism.
UR - http://www.scopus.com/inward/record.url?scp=84963904765&partnerID=8YFLogxK
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U2 - 10.1109/ECC.2015.7330973
DO - 10.1109/ECC.2015.7330973
M3 - Conference contribution
AN - SCOPUS:84963904765
T3 - 2015 European Control Conference, ECC 2015
SP - 2871
EP - 2877
BT - 2015 European Control Conference, ECC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - European Control Conference, ECC 2015
Y2 - 15 July 2015 through 17 July 2015
ER -