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Abstract: This paper presents a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback, and the emergence of multi-stability and associated hysteresis e#ects under positive feedback (Update)
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BibTeX entry: (Update)
D. Angeli and E.D. Sontag, Interconnections of monotone systems with steady-state characteristics, in Optimal Control, Stabilization, and Nonsmooth Analysis, Eds: de Queiroz, M., M. Maliso#, and P. Wolenski, Springer-Verlag, Heidelberg, 2004, pp. 135--154. http://citeseer.ist.psu.edu/angeli04interconnections.html More
@misc{ angeli04interconnections,
author = "D. Angeli and E. Sontag",
title = "Interconnections of monotone systems with steady-state characteristics",
text = "D. Angeli and E.D. Sontag, Interconnections of monotone systems with steady-state
characteristics, in Optimal Control, Stabilization, and Nonsmooth Analysis,
Eds: de Queiroz, M., M. Maliso#, and P. Wolenski, Springer-Verlag, Heidelberg,
2004, pp. 135--154.",
year = "2004",
url = "citeseer.ist.psu.edu/angeli04interconnections.html" }
Citations (may not include all citations):114 Mathematical Control Theory: Deterministic Finite Dimensiona.. (context) - Sontag - 1998
28 From molecular to modular cell biology (context) - Hartwell, Hopfield et al. - 1999
21 Stability Theory by Liapunov's Direct Method (context) - Rouche, Habets et al. - 1977
16 Monotone Dynamical Systems: An Introduction to the Theory of.. (context) - Smith - 1995
12 Construction of a genetic toggle switch in Escherichia coli (context) - Gardner, Cantor et al. - 2000
12 Emergent properties of networks of biological signaling path.. (context) - Bhalla, Iyengar - 1999
9 on monotone control systems - Angeli, Sontag et al. - 2002
4 Multi-stability in monotone Input/Output systems (context) - Angeli, Sontag - 2003
4 Ultrasensitivity in the mitogen-activated protein kinase cas.. (context) - C-Y - 1996
3 Early biological morphogenesis and nonlinear dynamics (context) - Hunding, Engelhardt - 1995
2 Positive and negative feedback: striking a balance between n.. - Cinquin, Demongeot - 2002
2 An analysis of a circadian model using the small-gain approa.. - Angeli, Sontag - 2003
2 Building a cell cycle oscillator: hysteresis and bistability.. (context) - Pomerening, Sontag et al. - 2003
2 Positive and negative circuits in dynamical systems - Gouze - 1998
2 Autocrine loop as a module for bidirectional and context-dep.. (context) - Shvartsman, Wiley et al. - 2000
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