@ARTICLE{IEEEsysbio_AS,
   AUTHOR       = {D. Angeli and E.D. Sontag},
   JOURNAL      = {IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology},
   TITLE        = {Oscillations in I/O monotone systems},
   YEAR         = {2008},
   OPTMONTH     = {},
   NOTE         = {Preprint version in arXiv q-bio.QM/0701018, 14 Jan 2007},
   OPTNUMBER    = {},
   PAGES        = {166-176},
   VOLUME       = {55},
   KEYWORDS     = {monotone systems, hopf bifurcations, circadian rhythms, 
      tridiagonal systems, nonlinear dynamics, systems biology, 
      biochemical networks, oscillations, periodic behavior},
   PDF          = {../../FTPDIR/angeli_sontag_circadian_TAC_CAS_2008.pdf},
   ABSTRACT     = {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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