Multi-stability in monotone input/output systems
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[1] U. Bhalla,et al. Emergent properties of networks of biological signaling pathways. , 1999, Science.
[2] David Angeli,et al. A remark on monotone control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..
[3] Xinzhi Liu. Comparison methods and stability theory , 1994 .
[4] Robert J. Plemmons,et al. Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.
[5] J. Collins,et al. Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.
[6] N. Rouche,et al. Stability Theory by Liapunov's Direct Method , 1977 .
[7] J. Borwein,et al. Convex Analysis And Nonlinear Optimization , 2000 .
[8] M. Hirsch. Stability and convergence in strongly monotone dynamical systems. , 1988 .
[9] Thomas Mestl,et al. FEEDBACK LOOPS, STABILITY AND MULTISTATIONARITY IN DYNAMICAL SYSTEMS , 1995 .
[10] Bruce Hannon,et al. Positive and Negative Feedback , 1994 .
[11] F R Adler,et al. How to make a biological switch. , 2000, Journal of theoretical biology.
[12] J. Gouzé. Positive and Negative Circuits in Dynamical Systems , 1998 .
[13] Hal L. Smith. Periodic tridiagonal competitive and cooperative systems of differential equations , 1991 .
[14] René Thomas. On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations , 1981 .
[15] Eduardo D. Sontag,et al. Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .
[16] James E. Ferrell,et al. Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible. , 2001, Chaos.
[17] John Ian Ferrell,et al. Detection of multi-stability , 2004 .
[18] R. Engelhardt,et al. EARLY BIOLOGICAL MORPHOGENESIS AND NONLINEAR DYNAMICS , 1995 .
[19] M Laurent,et al. Multistability: a major means of differentiation and evolution in biological systems. , 1999, Trends in biochemical sciences.
[20] J. Demongeot,et al. Positive and negative feedback: striking a balance between necessary antagonists. , 2002, Journal of theoretical biology.
[21] El Houssine Snoussi. Necessary Conditions for Multistationarity and Stable Periodicity , 1998 .
[22] S. Smale. On the differential equations of species in competition , 1976, Journal of mathematical biology.
[23] Rafael de la Llave,et al. On Irwin’s proof of the pseudostable manifold theorem , 1995 .
[24] Carlo Piccardi,et al. Remarks on excitability, stability and sign of equilibria in cooperative systems , 2002, Syst. Control. Lett..
[25] J E Ferrell,et al. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. , 1998, Science.
[26] H. Kunze,et al. A graph theoretical approach to monotonicity with respect to initial conditions II , 1999 .
[27] David Angeli,et al. Monotone control systems , 2003, IEEE Trans. Autom. Control..
[28] Eduardo Sontag,et al. Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 , 2003, Nature Cell Biology.
[29] M. Hirsch. Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere , 1985 .
[30] J. Smillie. Competitive and Cooperative Tridiagonal Systems of Differential Equations , 1984 .
[31] 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.
[32] Chris Cosner,et al. Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .
[33] W. Burridge,et al. “Excitability” , 1933 .