A controlled chaotic attractor could provide a tuneable oscillator for circadian clocks

References

• DE GOEDE , J. , OLOFSON , E. and RIETVELD , W. J. 1992 . A mathematical model of the circadian system with a delayed feedback loop . J. Interdisc. Cycle Res. , 23 : 142 – 144 .
   Web of Science ®Google Scholar
• DOWSE , H. and RINGO , J. 1992 . “ Do ultradian oscillators underlie the circadian clock in Drosophila ? ” . In Ultradian Rhythms in Life Processes , Edited by: LLOYD , D. and ROSSI , E.R. 105 – 117 . London : Springer‐Verlag .
   Google Scholar
• HARDIN , P.E. , HALL , J.C. and ROSBASH , M. 1992 . Circadian oscillators in period gene mRNA levels are transcriptionally regulated . Proc. Natl. Acad. Sci. USA , 89 : 11711 – 11715 .
   PubMed Web of Science ®Google Scholar
• HUNT , E.R. 1991 . Stabilizing high‐period orbits in a chaotic system: the diode resonator . Phys. Rev. Lett. , 67 : 1953 – 1955 .
   PubMed Web of Science ®Google Scholar
• LAKIN‐THOMAS , P.L. , BRODY , S. and COT , G. G. 1991 . Amplitude model for the effects of mutations and temperature on period and phase resetting of the Neurospora circadian oscillator . J. Biol. Rhythms , 6 : 281 – 297 .
   PubMed Web of Science ®Google Scholar
• LLOYD , A.L. and LLOYD , D. 1993 . Hypothesis: the central oscillator of the circadian clock is a controlled chaotic attractor . BioSystems , 29 : 77 – 85 .
   PubMed Web of Science ®Google Scholar
• OTT , E. , GREBOGI , C. and YORKE , J. A. 1990 . Controlling chaos . Phys. Rev. Lett. , 64 : 1196 – 1199 .
   PubMed Web of Science ®Google Scholar
• PITTENDRIGH , C. S. 1976 . “ Circadian clocks: what are they? ” . In The Molecular Basis of Circadian Rhythms , Edited by: HASTINGS , J.W. and SCHWEIGER , H.G. 11 – 48 . Berlin : Dahlem Konferenzen .
   Google Scholar
• PYRAGAS , K. 1992 . Continuous control of chaos by self‐controlling feedback . Phys. Lett. A , 170 : 421 – 428 .
   Web of Science ®Google Scholar
• SHINBROT , T. , GREBOGI , C. , OTT , E. and YORKE , J.A. 1993 . Using small perturbations to control chaos . Nature , 363 : 411 – 417 .
   Web of Science ®Google Scholar