Differential and graphical approaches to multistability theory for chemical reaction networks

@inproceedings{Lipson2007DifferentialAG,
  title={Differential and graphical approaches to multistability theory for chemical reaction networks},
  author={Mark Lipson},
  year={2007}
}
The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and expand upon the body of mathematical results pertaining to the theory of multiple equilibria in chemical reaction networks (CRNs), which has yielded surprising insights with minimal computational effort. Our central focus is a recent, cycle-based theorem by… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 54 REFERENCES

Positive and negative feedback: striking a balance between necessary antagonists.

Cinquin, Olivier, Jacques Demongeot
  • Journal of Theoretical Biology
  • 2002
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Multisite protein phosphorylation makes a good threshold but can be a poor switch.

  • Proceedings of the National Academy of Sciences of the United States of America
  • 2005
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems.

David Angeli, Ferrell, E. James, Eduardo Sontag
  • Proceedings of the National Academy of Sciences
  • 2004
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Monotone control systems

  • IEEE Trans. Automat. Contr.
  • 2002
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL