David Corfield Dynamical systems

References

Monotone

• Hal L. Smith, 2017, Monotone dynamical systems: Reflections on new advances & applications, Volume 37, Issue 1: 485-504. Doi: 10.3934/dcds.2017020

• David Angeli, Eduardo D. Sontag, Monotone Control Systems, arXiv:math/0206133

• Angeli, D. (2021). Monotone Systems in Biology. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_90

Hirsch and Smith, Monotone dynamical systems (Handbook of Differential Equations, 2005)

Smith’s monograph Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems (AMS Surveys and Monographs 41, 1995)

“generic convergence”: almost every trajectory converges to an equilibrium — they cannot have stable oscillations or chaos.

De Leenheer, Angeli, and Sontag, “A tutorial on monotone systems — with an application to chemical reaction networks,

Sontag, Some new directions in control theory inspired by systems biology“ (IEE Proc. Systems Biology 1:9–18, 2004)

Angeli, Ferrell, and Sontag, “Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems,” Proc. Natl. Acad. Sci. USA 101:1822–1827 (2004)

Angeli, D., Sontag, E. Interconnections of Monotone Systems with Steady-State Characteristics. In: de Queiroz, M.S., Malisoff, M., Wolenski, P. (eds) Optimal Control, Stabilization and Nonsmooth Analysis. Lecture Notes in Control and Information Science, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39983-4_9

and “Multi-stability in monotone input/output systems,” Systems and Control Letters 51:185–202 (2004). https://arxiv.org/abs/q-bio/0309002 This is exactly the assume-guarantee/compositional-certificate structure from our recent turns, in its biological-control incarnation

Enciso, Smith, and Sontag, “Non-monotone systems decomposable into monotone systems with negative feedback”,

Angeli–Sontag, “Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles,” Nonlinear Analysis Series B, 2008)

Angeli, De Leenheer, and Sontag, “A Petri net approach to the study of persistence in chemical reaction networks” (arXiv q-bio/0608019, 2006) uses Petri-net structure (the T-invariants/P-invariants and siphons we discussed) to prove persistence — that no species goes extinct — which complements the monotone-convergence results.

Sontag, E. Monotone and near-monotone network structure (part I), https://arxiv.org/abs/q-bio/0612032

Sontag, E. Monotone and near-monotone network structure (part II) https://arxiv.org/abs/q-bio/0612033