Stability of Equilibria for Hybrid Models of Genetic Regulatory Networks

[1]  Martin Fussenegger,et al.  Modeling the Quorum Sensing Regulatory Network of Human‐Pathogenic Pseudomonas aeruginosa , 2004, Biotechnology progress.

[2]  Claire J. Tomlin,et al.  Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model , 2001, HSCC.

[3]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[4]  G. Yagil,et al.  On the relation between effector concentration and the rate of induced enzyme synthesis. , 1971, Biophysical journal.

[5]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[6]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[7]  T. Mestl,et al.  A mathematical framework for describing and analysing gene regulatory networks. , 1995, Journal of theoretical biology.

[8]  S. Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1987 .

[9]  H. D. Jong,et al.  Piecewise-linear Models of Genetic Regulatory Networks: Equilibria and their Stability , 2006, Journal of mathematical biology.

[10]  T. Mestl,et al.  Periodic solutions in systems of piecewise- linear differential equations , 1995 .

[11]  Fotios Giannakopoulos,et al.  Planar systems of piecewise linear differential equations with a line of discontinuity , 2001 .

[12]  R Thomas,et al.  Dynamical behaviour of biological regulatory networks--I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. , 1995, Bulletin of mathematical biology.

[13]  K. Kohn.  Molecular interaction maps as information organizers and simulation guides. , 2001, Chaos.

[14]  Calin Belta,et al.  Hybrid Modeling and Simulation of Biomolecular Networks , 2001, HSCC.

[15]  Thomas Mestl,et al.  Global analysis of steady points for systems of differential equations with sigmoid interactions , 1994 .

[16]  J. Gouzé,et al.  A class of piecewise linear differential equations arising in biological models , 2002 .

[17]  L. Glass,et al.  Stable oscillations in mathematical models of biological control systems , 1978 .

[18]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[19]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[20]  L. I. Reyes,et al.  Exact solutions to chaotic and stochastic systems. , 2001, Chaos.

[21]  Hidde de Jong,et al.  Genetic Network Analyzer: qualitative simulation of genetic regulatory networks , 2003, Bioinform..

[22]  H. D. Jong,et al.  Qualitative simulation of the initiation of sporulation in Bacillus subtilis , 2004, Bulletin of mathematical biology.

[23]  L. Glass,et al.  The logical analysis of continuous, non-linear biochemical control networks. , 1973, Journal of theoretical biology.

[24]  R. Edwards.  Analysis of continuous-time switching networks , 2000 .