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Continuous growth models in terms of generalized logarithm and exponential functions

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  • Martinez, Alexandre Souto
  • González, Rodrigo Silva
  • Terçariol, César Augusto Sangaletti
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    Abstract

    Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and unify the great majority of continuous growth models, which we briefly review. Physical interpretation to the generalization function parameter is given for the Richards’ model, which has an underlying microscopic model to justify it.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 387 (2008)
    Issue (Month): 23 ()
    Pages: 5679-5687

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    Handle: RePEc:eee:phsmap:v:387:y:2008:i:23:p:5679-5687

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Population dynamics; Generalized logarithmic and exponential functions; Growth models; Richard’s model; Marusic and Bajzer’s model; Tsoularis and Wallace’s model;

    References

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    1. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2008. "Psychophysics of time perception and intertemporal choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2066-2074.
    2. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    3. Takahashi, Taiki, 2007. "A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 637-644.
    4. Kalogeropoulos, Nikos, 2005. "Algebra and calculus for Tsallis thermo-statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 408-418.
    5. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2007. "Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 338-342.
    6. Takahashi, Taiki, 2008. "A comparison between Tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 551-556.
    7. Takahashi, Taiki, 2007. "A probabilistic choice model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 335-338.
    8. Cajueiro, Daniel O., 2006. "A note on the relevance of the q-exponential function in the context of intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 385-388.
    9. de Jesus Holanda, Adriano & Torres Pisa, Ivan & Kinouchi, Osame & Souto Martinez, Alexandre & Eduardo Seron Ruiz, Evandro, 2004. "Thesaurus as a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 530-536.
    10. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
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    Citations

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    Cited by:
    1. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.
    2. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    3. Rivera-Castro, Miguel A. & Miranda, José G.V. & Borges, Ernesto P. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "A top–bottom price approach to understanding financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1489-1496.
    4. Cabella, Brenno Caetano Troca & Ribeiro, Fabiano & Martinez, Alexandre Souto, 2012. "Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1281-1286.

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