TY - GEN
T1 - Saddle-node bifurcation and its robustness analysis
T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
AU - Inoue, Masaki
AU - Imura, Jun Ichi
AU - Arai, Takayuki
AU - Kashima, Kenji
AU - Aihara, Kazuyuki
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014
Y1 - 2014
N2 - In this paper, we study saddle-node bifurcation and its robustness analysis for a class of nonlinear systems with dynamic uncertainties. First, we formulate a robust bifurcation analysis problem of evaluating the region that contains all potential bifurcation points on which an equilibrium appears, disappears, or loses hyperbolicity depending on uncertainties. Next, we propose an existence condition of multiple equilibria and evaluation of their location. Then, we derive a condition for robust hyperbolicity of a set of potential equilibrium points, and identify the region that contains all potential bifurcation points. The proposed analysis method is applied to robustness analysis of a genetic network model representing a mechanism for generating induced pluripotent stem cells (iPS cells). We find that saddle-node bifurcation occurs in the iPS model. Then, by the proposed robustness analysis, we further show that the bifurcation is so robust that it plays an essential role for inducing pluripotency in actual iPS cells.
AB - In this paper, we study saddle-node bifurcation and its robustness analysis for a class of nonlinear systems with dynamic uncertainties. First, we formulate a robust bifurcation analysis problem of evaluating the region that contains all potential bifurcation points on which an equilibrium appears, disappears, or loses hyperbolicity depending on uncertainties. Next, we propose an existence condition of multiple equilibria and evaluation of their location. Then, we derive a condition for robust hyperbolicity of a set of potential equilibrium points, and identify the region that contains all potential bifurcation points. The proposed analysis method is applied to robustness analysis of a genetic network model representing a mechanism for generating induced pluripotent stem cells (iPS cells). We find that saddle-node bifurcation occurs in the iPS model. Then, by the proposed robustness analysis, we further show that the bifurcation is so robust that it plays an essential role for inducing pluripotency in actual iPS cells.
UR - http://www.scopus.com/inward/record.url?scp=84963824720&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84963824720&partnerID=8YFLogxK
U2 - 10.1109/CDC.2014.7040324
DO - 10.1109/CDC.2014.7040324
M3 - Conference contribution
AN - SCOPUS:84963824720
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5973
EP - 5978
BT - 53rd IEEE Conference on Decision and Control,CDC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 15 December 2014 through 17 December 2014
ER -