References
- L. Von Bertalanffy . Quantitative laws in metabolism and growth . The Quarterly Review of Biology , 32 : 217 – 231 , 1957 . http://dx.doi.org/10.1086/401873
- J.E. Bullard , G.H. Mctainsh and P. Martin . Establishing stage-discharge relationships in multiple-channelled, ephemeral rivers: a case study of the Diamantina River . Geographical Research , 45 : 233 – 245 , 2007 . http://dx.doi.org/10.1111/j.1745-5871.2007.00457.x .
- J. Callede , P. Kosuth and E. de Oliveira . Établissement de la relation hauteurdébit de l'Amazone à Obidos: méthode de la dénivelée normale à “géométrie variable” . Hydrological Sci. J. , 46 : 451 – 463 , 2001 . http://dx.doi.org/10.1080/02626660109492838
- Dubeau , F. and Mir , Y. 2011 . Least squares fitting with single inflection point growth curve I – The models . Math. Model. Appl. Comput. , 2 : 269 – 281 .
- Dubeau , F. , Mir , Y. , Assani , A.A. and Chalifour , A. 2011 . Least squares fitting with single inflection point growth curve II – An application . Math. Model. Appl. Comput. , 2 : 283 – 301 .
- F. Dubeau , Y. Mir , A.A. Assani and A. Chalifour . Modelling stage-discharge relationship with single inflection point nonlinear functions . Int. J. Hydrology Sci. Technol. , 2 : 153 – 167 , 2012 . http://dx.doi.org/10.1504/IJHST.2012.047430
- E.H. Habid and E.A. Meselhe . Stage-Discharge relations for low-gradient tidal streams using data-driver models . ASCE J. Hydraul. Eng. , 132 : 482 – 492 , 2006 . http://dx.doi.org/10.1061/(ASCE)0733-9429(2006)132:5(482) .
- Huet , S. , Jolivet , E. and Messéan , A. 1992 . La régression non linéaire: méthodes et applications en biologie , Paris : INRA .
- Z. Ismail , A. Khamis and M.Y. Jaafar . Fitting nonlinear Gompertz curve to tobacco growth data . Pakistan J. Agronomy , 2 : 223 – 236 , 2003 . http://dx.doi.org/10.3923/ja.2003.223.236
- R.C. Jain , R. Agrawal and K.N. Singh . A whitin year growth model for crop yield forecasting . Biom. J. , 34 : 789 – 799 , 1992 . http://dx.doi.org/10.1002/bimj.4710340705
- A. Khamis , Z. Ismail , K. Haron and A.T.M. Mohammed . Nonlinear growth models for modeling oil palm yield growth . J. Math. Stat. , 1 : 225 – 233 , 2005 . http://dx.doi.org/10.3844/jmssp.2005.225.233
- H.D. Kuhi , T. Porter , S. López , E. Kebreab , A.B. Strathe , A. Dumas , J. Dijkstra and J. France . A review of mathematical functions for the analysis of growth in poultry . World's Poultry Sci. J. , 66 : 227 – 239 , 2010 . http://dx.doi.org/10.1017/S0043933910000280
- H. Liao and D.W. Knight . Analytic stage-discharge formulae for flow in straight trapezoidal open channels . Adv. Water Resour. , 30 : 2283 – 2295 , 2007 . http://dx.doi.org/10.1016/j.advwatres.2007.05.002
- A.S. Martinez , R.S. Gonzalez and C.A.S. Tercariol . Continuous qrowth models in terms of generalized logarithm and exponential functions . Phys. A , 387 : 5679 – 5687 , 2008 . http://dx.doi.org/10.1016/j.physa.2008.06.015
- M. Marusic and Z. Bajzer . Generalized two-parameter equation of growth . J. Math. Anal. Appl. , 179 : 446 – 462 , 1993 . http://dx.doi.org/10.1006/jmaa.1993.1361 .
- P.S. Meyer and J.H. Ausubel . Carrying capacity: a model with logistically varying limits . Technological Forecasting and Social Change , 61 : 209 – 214 , 1999 . http://dx.doi.org/10.1016/S0040-1625(99)00022-0 .
- P.S. Meyer , J.W. Yung and J.H. Ausubel . A primer on logistic growth and substitution: the mathematics of the Loglet Lab Software . Technological Forecasting and Social Change , 61 : 247 – 271 , 1999 . http://dx.doi.org/10.1016/S0040-1625(99)00021-9 .
- M.M. Mischan , S.Z. Pinho and L.R. Carvalho . Determination of a point sufficiently close to the asymptote in nonlinear growth functions . Sci. Agric. (Piracicaba, Braz.) , 68 : 109 – 114 , 2011 . http://dx.doi.org/10.1590/S0103-90162011000100016 .
- P.H. Morgan , L.P. Mercer and N.W. Flodin . General model for nutritional response of higher organisms . Proc. Nat. Acad. Sci. USA , 72 : 4327 – 4331 , 1975 . http://dx.doi.org/10.1073/pnas.72.11.4327
- Murray , J.D. 1989 . Mathematical Biology , Berlin : Springel .
- A. Petersen-Overleir . Modelling stage-discharge relationships affected by hysteresis using the Jones formula and nonlinear regression . Hydrological Sci. J. , 51 : 365 – 388 , 2006 . http://dx.doi.org/10.1623/hysj.51.3.365 .
- Philip , M.S. 1994 . Measuring Trees and Forests, , 2nd ed , Wallingford , , UK : CAB International .
- Ratkowsky , D.A. 1983 . Nonlinear Regression Modeling , New York : Marcel Dekker .
- Ratkowsky , D.A. 1989 . Handbook of Nonlinear Regression Models , New York : Marcel Dekker .
- J. Schnute . A versatile growth model with statistically stable parameters . Canad. J. Fisheries and Aquatic Sci. , 38 : 1128 – 1140 , 1981 . http://dx.doi.org/10.1139/f81-153
- R. Scitovski and D. Jukic . A method for solving the parameter identification problem for ordinary differential equations of the second order . Appl. Math. Comput. , 74 : 273 – 291 , 1996 . http://dx.doi.org/10.1016/0096-3003(95)00098-4 .
- Scitovski , R. and Kosanovic , S. 1985 . Rate of change in economics research . Economics Anal. , 19 : 65 – 73 .
- Seber , G.A.F. and Wild , C.J. 1989 . Nonlinear Regression , New York : John Wiley & Sons .
- Shepherd , J.J. and Stojkov , L. 2007 . The logistic population model with slowly varying carrying capacity . ANZIAM J. , 47 : 492 – 506 .
- J. Tobin . Estimation of relationships for limited dependent variables . Econometrica , 26 : 24 – 36 , 1958 . http://dx.doi.org/10.2307/1907382
- A. Tsoularis and J. Wallace . Analysis of logistic growth models . Math. Biosci. , 179 : 21 – 55 , 2002 . http://dx.doi.org/10.1016/S0025-5564(02)00096-2 .
- J.A. Westphal , D.B. Thompson , G.T. Stevens Jr . and C.N. Strauser . Stage-Discharge relations on the middle Mississippi River . J. Water Resour. Plann. Manage. , 125 : 48 – 53 , 1999 . http://dx.doi.org/10.1061/(ASCE)0733-9496(1999)125:1(48) .
- L. Yuancai , C.P. Marques and F.W. Macedo . Comparaison of Schnute's and Bertalanffy-Richards’ growth function . Forest Ecology and Management , 96 : 283 – 288 , 1997 . http://dx.doi.org/10.1016/S0378-1127(96)03966-7 .
- Zeide , B. 1993 . Analysis of growth equations . Forest Sci. , 39 : 594 – 616 .
- L. Zhang . Cross-validation of non-linear growth functions for modelling tree height-diameter relationships . Ann. Bot. , 79 : 251 – 257 , 1997 . http://dx.doi.org/10.1006/anbo.1996.0334