M. Hirsch, H. Smith, et al., "Monotone dynamical systems," Handbook of differential equations: ordinary differential equations, Vol. 2, pp. 239-357, 2005.
D. Angeli and E. Sontag, "Monotone control systems," IEEE Trans. Autom. Control, Vol. 48, no. 10, pp. 1684-1698, 2003.
E. D. Sontag, "Monotone and near-monotone biochemical networks," Systems and Synthetic Biology, Vol. 1, no. 2, pp. 59-87, 2007.
N. Ramdani, N. Meslem, and Y. Candau, "Computing reachable sets for uncertain nonlinear monotone systems," Nonlinear Analysis: Hybrid Systems, Vol. 4, no. 2, pp. 263-278, 2010.
A. Sootla, D. Oyarzún, D. Angeli, and G.-B. Stan, "Shaping pulses to control bi-stable biological systems," http://arxiv.org/abs/1409.6150, 2014.
P.-J. Meyer, A. Girard, and E. Witrant, "Controllability and invariance of monotone systems for robust ventilation automation in buildings," in Proc. Conf, Decision Control. IEEE, 2013, pp. 1289-1294.
L. Chisci and P. Falugi, "Asymptotic tracking for constrained monotone systems," Automatic Control, IEEE Transactions on, Vol. 51, no. 5, pp. 873-879, 2006.
A. Sootla and J. Anderson, "On projection-based model reduction of biochemical networks-part i: The deterministic case," in Proc Conf Decison Control, dec 2014, pp. 3615-3620.
-, "On projection-based model reduction of biochemical networks-part II: The stochstic case," in Proc Conf Decison Control, dec 2014, pp. 3621-3626.
G. I. Kalmykov, "On the partial ordering of one-dimensional Markov processes," Theory of Probability & Its Applications, Vol. 7, no. 4, pp. 456-459, 1962.
D. Daley, "Stochastically monotone markov chains," Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 10, no. 4, pp. 305-317, 1968.
A. Müller and D. Stoyan, Comparison methods forstochastic models and risks., 2002.
D. Stoyan and D. J. Daley, "Comparison methods for queues and other stochastic models." John Wiley & Sons, Inc., 605 Third Ave., New York, NY 10158, USA, 1983, 1983.
J. Bergenthum, L. Rüschendorf, et al., "Comparison of semimartingales and lévy processes," The Annals of Probability, Vol. 35, no. 1, pp. 228-254, 2007.
M. Keller-Ressel, E. Mayerhofer, and A. G. Smirnov, "On convexity of solutions of ordinary differential equations," Journal of Mathematical Analysis and Applications, Vol. 368, no. 1, pp. 247-253, 2010.
A. Rantzer and B. Bernhardsson, "Control of convex monotone systems," in In Proc Conf Decision Control, Los Angeles, CA, USA, 2014.
A. Sootla, "On monotonicity and propagation of order properties," Arxiv preprint arXiv:1503.02557, March 2015.
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry. Elsevier, 2007.
D. T. Gillespie, "The chemical langevin equation," J. Chem. Phys., Vol. 113, p. 297, 2000.
H. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. American Mathematical Soc., 2008, vol. 41.
M. Shaked and J. G. Shanthikumar, Stochastic orders. Springer, 2007.
T. Gardner, C. R. Cantor, and J. J. Collins, "Construction of a genetic toggle switch in escherichia coli," Nature, Vol. 403, pp. 339-342, 2000.
A. Levskaya, O. D. Weiner, W. A. Lim, and C. A. Voigt, "Spatiotemporal control of cell signalling using a light-switchable protein interaction," Nature, Vol. 461, pp. 997-1001, 2009.
B. Øksendal, Stochastic differential equations. Springer, 2003.
I. Herbst and L. Pitt, "Diffusion equation techniques in stochastic monotonicity and positive correlations," Probability theory and related fields, Vol. 87, no. 3, pp. 275-312, 1991.
