Universality in nonlinear prediction of complex systems

References

• Bramwell , S.T. , Holdsworth , P.C.W. and Pinton , J.F. 1998 . Universality of rare fluctuations in turbulence and critical phenomena . Nature , 396 : 552 – 554 .
   Google Scholar
• Bramwell , S.T. , Christensen , K. , Fortin , J.Y. , Holdsworth , P.C.W. , Jensen , H.J. , Lise , S. , López , J.M. , Nicodemi , M. and Sellitto , M. 2001 . Universal fluctuations in correlated systems . Phys. Rev. Lett. , 84 : 3744 – 3747 .
   Google Scholar
• Bramwell , S.T. , Fortin , J.Y. , Holdsworth , P.C.W. , Peysson , S. , Pinton , J.F. , Portelli , B. and Sellitto , M. 2001 . Magnetic fluctuations in the classical XY model: The origin of an exponential tail in a complex system . Phys. Rev. E , 63 041106
   Google Scholar
• Bramwell , S.T. , Fennell , T. , Holdsworth , P.C.W. and Portelli , B. 2002 . Universal fluctuations of the danube water level: A link with turbulence, criticality and company growth . Europhys. Lett. , 57 : 310
   Google Scholar
• Dahlstedt , K. and Jensen , H.J. 2005 . Fluctuation spectrum and size scaling of river flow and level . Phys. A , 348 : 596 – 610 .
   Google Scholar
• Gonçalves , R. , Pinto , A. and Calheiros , F. 2007 . “ Comparison of methodologies in riverflow prediction. The river Paiva case ” . In Mathematical Methods in Engineering , 361 – 370 . New York, NY : Springer .
   Google Scholar
• Gonçalves , R. , Pinto , A. and Calheiros , F. 2007 . “ Nonlinear prediction of riverflow. The river Paiva case ” . In Views on Ordinary Differential Equations , 231 – 240 . Basle : Birkhaüser .
   Google Scholar
• Gonçalves , R. , Pinto , A. and Stollenwerk , N. 2009 . Cycles and universality in sunspot numbers fluctuations . Astrophys. J. , 691 : 1583 – 1586 .
   Google Scholar
• R. Gonçalves, A. Pinto, and N. Stollenwerk, The Gaussian and the BHP distribution in riverflow (2009), in preparation
   Google Scholar
• Islam , S. and Sivakumar , B. 2002 . Characterization and prediction of runoff dynamics: A nonlinear dynamical view . Adv. Water Resour. , 25 : 179 – 190 .
   Google Scholar
• Jayawardena , A. and Gurung , A. 2000 . Noise reduction and prediction of hydrometereological time series dynamical systems approach vs stochastic approach . J. Hydrol. , 228 : 242 – 264 .
   Web of Science ®Google Scholar
• Jayawardena , A.W. and Lai , F. 1994 . Analysis and prediction of chaos in rainfall and stream flow time series . J. Hydrol. , 153 : 23 – 52 .
   Web of Science ®Google Scholar
• Jayawardena , A. , Li , W. and Xu , P. 2002 . Neighbourhood selection for local modelling and prediction of hydrological time series . J. Hydrol. , 258 : 40 – 57 .
   Google Scholar
• Kantz , H. and Schreiber , T. 1997 . Nonlinear Time Series Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Kennel , M. , Brown , R. and Abarbanel , H. 1992 . Determining minimum embedding dimension for phase space reconstruction using a geometrical construction . Phys. Rev. E , 48 ( 3 ) : 1752 – 1763 .
   Google Scholar
• Liu , Q. , Islam , S. , Rodriguez-Iturbe , I. and Le , Y. 1998 . Phase-space analysis of daily streamflow: Characterization and prediction . Adv. Water Resour. , 210 : 463 – 475 .
   Google Scholar
• Lorenz , E. 1969 . Atmospheric predictability as revealed by naturally ocurring analogues . J. Atmos. Sci. , 20 : 636 – 646 .
   Google Scholar
• van Milligen , B.Ph. , Sánchez , R. , Carreras , B.A. , Lynch , V.E. , LaBombard , B. , Pedrosa , M.A. , Hidalgo , C. , Gonçalves , B. and Balbín , R. 2005 . Additional evidence for the universality of turbulent fluctuations and fluxes in the scrape-off layer of tokamaks and stellarators . Phys. Plasmas , 12 05207
   Google Scholar
• Pikovski , A. 1986 . Discrete-time dynamic noise filtering . Sov. J. Commun. Technol. Electr. , : 31 – 81 .
   Google Scholar
• Porporato , L. and Ridolfi , L. 1996 . Clues to the existence of deterministic chaos in river flow . Int. J. Mod. Phys. B , 100 : 1821 – 1862 .
   Google Scholar
• Porporato , L. and Ridolfi , L. 1997 . Nonlinear analysis of a river flow time sequences . Water Resour. Res. , 33 : 1353 – 1367 .
   Web of Science ®Google Scholar
• Sinha-Ray , P. , Borda de Água , L. and Jensen , H.J. 2001 . Threshold dynamics, multifractality and universal fluctuations in the SOC forest fire: Facets of an auto-ignition model . Phys. D , 157 : 186 – 196 .
   Google Scholar
• Takens , F. 1980 . “ Detecting strange attractors in turbulence ” . In Lecture Notes in Mathematics , Edited by: Rand , D.A. and Young , L. Vol. 898 , 366 – 381 . New York, NY : Springer .
   Google Scholar