References
- Aggrey, S. E. 2002. Comparison of three nonlinear and spline regression models for describing chicken growth curves. Poultry Science 81 (12):1782–8. doi:https://doi.org/10.1093/ps/81.12.1782.
- Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–22. doi:https://doi.org/10.1109/TAC.1974.1100705.
- Birch, C. P. D. 1999. A new generalized logistic sigmoid growth equation compared with the Richards growth equation. Annals of Botany 83 (6):713–23. doi:https://doi.org/10.1006/anbo.1999.0877.
- Coleman, B. D. 1981. On optimal intrinsic growth rates for populations in periodically changing environments. Journal of Mathematical Biology 12 (3):343–54. doi:https://doi.org/10.1007/BF00276921.
- Coleman, T. F., and Y. Li. 1994. On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds. Mathematical Programming 67 (1–3):189–224. doi:https://doi.org/10.1007/BF01582221.
- Coleman, T. F., and Y. Li. 1996. An interior trust region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization 6 (2):418–45. doi:https://doi.org/10.1137/0806023.
- Dubeau, F., and Y. Mir. 2013. Growth models with oblique asymptote. Mathematical Modelling and Analysis 8:204–18. doi:https://doi.org/10.3846/13926292.2013.781068.
- Huet, S., E. Jolivet, and A. Messéan. 1992. La régression non linéaire: Méthodes et application en biologie. Paris, France: INRA.
- Jain, R. C., R. Agrawal, and K. N. Singh. 1992. A within year growth model for crop yield forecasting. Biometrical Journal 34 (7):789–99. doi:https://doi.org/10.1002/bimj.4710340705.
- Karaman, E., D. Narinc, M. Z. Firat, and T. Aksoy. 2013. Nonlinear mixed effects modeling of growth in Japanese quail. Poultry Science Association 92 (7):1942–8. doi:https://doi.org/10.3382/ps.2012-02896.
- Khamis, A., Z. Ismail, K. Haron, and A. T. M. Mohammed. 2005. Nonlinear growth models for modeling oil palm yield growth. Journal of Mathematics and Statistics 1:225–33. doi:https://doi.org/10.3844/jmssp.2005.225.232.
- Koops, W. J. 1986. Multiphasic growth curve analysis. Growth 50:169–77.
- Kuhi, H. D., T. Porter, S. López, E. Kebreab, A. B. Strathe, A. Dumas, J. Dijkstra, and J. France. 2010. A review of mathematical functions for the analysis of growth in poultry. World’s Poultry Science Journal 66:227–39. doi:https://doi.org/10.1017/S0043933910000280.
- Marusic, M., and Z. Bajzer. 1993. Generalized two-parameter equation of growth. Journal of Mathematical Analysis and Applications 179 (2):446–62. doi:https://doi.org/10.1006/jmaa.1993.1361.
- Mir, Y. 2015. Approximate solutions to some non-autonomous differential equations for growth phenomena. Surveys in Mathematics & Its Applications 10:139–48.
- Mir, Y., and F. Dubeau. 2015. Least squares fitting of the stage-discharge relationship using smooth models with curvilinear asymptotes. Hydrological Sciences Journal 60 (10):1797–812. doi:https://doi.org/10.1080/02626667.2014.935779.
- Mir, Y., and F. Dubeau. 2016. On the linear and logistic models with time dependent coefficients. Electronic Journal of Differential Equations 2016:1–17.
- Murray, J. D. 1989. Mathematical biology. Berlin, Germany: Springer.
- Narinc, D., E. Karaman, M. Z. Firat, and T. Aksoy. 2010. Comparison of non-linear growth models to describe the growth in japanese quail. Journal of Animal and Veterinary Advances 9:1961–6. doi:https://doi.org/10.3923/javaa.2010.1961.1966.
- Nesetrilova, H. 2005. Multiphasic growth models for cattle. Czech Journal of Animal Science 8:347–54.
- Ratkowsky, D. A. 1983. Nonlinear regression modeling. New York, NY: Marcel Dekker.
- Ratkowsky, D. A. 1989. Handbook of nonlinear regression models. New York, NY: Marcel Dekker.
- Ricker, W. E. 1979. Growth rates and models. In Fish physiology: Bioenergetics and growth, eds. W. S. Hoar, D. J. Randall, and J. R. Brett, 677–753. Orlando, FL: Academic Press Inc.
- Rogovchenko, S. P., and Y. V. Rogovchenko. 2009. Effect of periodic environmental fluctuations on the pearl-verhulst model. Chaos, Solitons and Fractals 39 (3):1169–81. doi:https://doi.org/10.1016/j.chaos.2007.11.002.
- Roush, W. B., W. A. Dozier, and S. L. Branton. 2006. Gompertz and neural network models of broiler growth. Poultry Science 85 (4):794–7. doi:https://doi.org/10.1093/ps/85.4.794.
- Schnute, J. 1981. A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38 (9):1128–40. doi:https://doi.org/10.1139/f81-153.
- Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2):461–4. doi:https://doi.org/10.1214/aos/1176344136.
- Seber, G. A. F., and C. J. Wild. 1989. Nonlinear regression. New York, NY: John Wiley & Sons.
- Tsoularis, A., and J. Wallace. 2002. Analysis of logistic growth models. Mathematical Biosciences 179 (1):21–55. doi:https://doi.org/10.1016/S0025-5564(02)00096-2.
- Yuancai, L., C. P. Marques, and F. W. Macedo. 1997. Comparaison of Schnute’s and Bertalanffy-Richards’ growth function. Forest Ecology and Management 96 (3):283–8. doi:https://doi.org/10.1016/S0378-1127(96)03966-7.
- Zhang, L. 1997. Cross-validation of non-linear growth functions for modelling tree height-diameter relationships. Annals of Botany 79 (3):251–7. doi:https://doi.org/10.1006/anbo.1996.0334.