Publications about 'hopf bifurcations'
Articles in journal or book chapters
  1. D. Angeli and E.D. Sontag. Oscillations in I/O monotone systems. IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology, 55:166-176, 2008. Note: Preprint version in arXiv q-bio.QM/0701018, 14 Jan 2007. [PDF] Keyword(s): monotone systems, hopf bifurcations, circadian rhythms, tridiagonal systems, nonlinear dynamics, systems biology, biochemical networks, oscillations, periodic behavior, delay-differential systems.
    In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, based on the application of a tight small gain condition. This stability persists even under arbitrary delays in the feedback loop. On the other hand, when the condition is violated a Poincare'-Bendixson result allows to conclude existence of oscillations, for sufficiently high delays.



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Last modified: Sat Dec 2 22:29:19 2023
Author: sontag.

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