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Towards possible q-generalizations of the Malthus and Verhulst growth models

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  • Strzałka, Dominik
  • Grabowski, Franciszek

Abstract

Tsallis entropy introduced in 1988 based on the equation Sq=1−∑ipiqq−1 has been considered to obtain new possibilities for constructing a generalized thermodynamical basis for statistical physics, expanding classical Boltzmann–Gibbs thermodynamics for non-equilibrium states. During the last two decades this q-generalized theory has been successfully applied to a considerable amount of physically interesting complex phenomena. The authors wish to present a mathematical analysis of the possible q-generalizations of the Malthus and the Verhulst growth models based on Tsallis definitions of the q-logarithm and the q-exponential.

Suggested Citation

  • Strzałka, Dominik & Grabowski, Franciszek, 2008. "Towards possible q-generalizations of the Malthus and Verhulst growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2511-2518.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2511-2518
    DOI: 10.1016/j.physa.2007.12.014
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
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    Cited by:

    1. Ribeiro, Fabiano L. & Ribeiro, Kayo N., 2015. "A one dimensional model of population growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 201-210.
    2. 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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