Abstract
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.
| Original language | English |
|---|---|
| Article number | 7040324 |
| Pages (from-to) | 5973-5978 |
| Number of pages | 6 |
| Journal | Unknown Journal |
| Volume | 2015-February |
| Issue number | February |
| DOIs | |
| Publication status | Published - 2014 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization
Cite this
Saddle-node bifurcation and its robustness analysis : A mechanism for inducing pluripotency in stem cell. / Inoue, Masaki; Imura, Jun Ichi; Arai, Takayuki; Kashima, Kenji; Aihara, Kazuyuki.
In: Unknown Journal, Vol. 2015-February, No. February, 7040324, 2014, p. 5973-5978.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Saddle-node bifurcation and its robustness analysis
T2 - A mechanism for inducing pluripotency in stem cell
AU - Inoue, Masaki
AU - Imura, Jun Ichi
AU - Arai, Takayuki
AU - Kashima, Kenji
AU - Aihara, Kazuyuki
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 - Article
AN - SCOPUS:84963824720
VL - 2015-February
SP - 5973
EP - 5978
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
SN - 0165-4896
IS - February
M1 - 7040324
ER -