A note on multistability and monotone I/O systems

Multi-stability and hysteresis are important systems properties in many applications, and particularly in biology. This paper studies such properties in the framework of monotone systems with well-defined steady-state responses. Characterizations of global stability behavior are stated in terms of easily checkable graphical conditions.

[1]  Eduardo Sontag,et al.  Untangling the wires: A strategy to trace functional interactions in signaling and gene networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[2]  David Angeli,et al.  Monotone control systems , 2003, IEEE Trans. Autom. Control..

[3]  H. Kunze,et al.  A graph theoretical approach to monotonicity with respect to initial conditions II , 1999 .

[4]  J. Gouzé.  Positive and Negative Circuits in Dynamical Systems , 1998 .

[5]  Hal L. Smith.  Periodic tridiagonal competitive and cooperative systems of differential equations , 1991 .

[6]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[7]  Eduardo Sontag,et al.  Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 , 2003, Nature Cell Biology.

[8]  David Angeli,et al.  A remark on monotone control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[10]  Carlo Piccardi,et al.  Remarks on excitability, stability and sign of equilibria in cooperative systems , 2002, Syst. Control. Lett..

[11]  M Laurent,et al.  Multistability: a major means of differentiation and evolution in biological systems. , 1999, Trends in biochemical sciences.

[12]  Chris Cosner,et al.  Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .

[13]  James E. Ferrell,et al.  Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible. , 2001, Chaos.