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A one dimensional model of population growth

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  • Ribeiro, Fabiano L.
  • Ribeiro, Kayo N.

Abstract

In this work, a one dimensional population growth model is proposed. The model, based on the cooperative and competitive individual–individual distance-dependent interaction, allows us to get a full analytical solution. With this analytical approach, it was possible to investigate the dynamics of the population according to some parameters, as intrinsic growth rate, strength of the interaction between individuals, and the distance-dependent interaction. As a consequence of the individuals’ interaction, a rich phase diagram to which the population has access was observed. The phases observed are: convergence to carrying capacity, exponential growth, divergence at finite time, and extinction. Moreover, it was also observed that some phases are strictly dependent on the initial condition. For instance, in the cooperative regime with negative intrinsic growth rate, the population can diverge or become extinct according to the initial population size. The phases accessible to the population can be seen as a macroscopic behavior which emerges from the interaction among the individuals (the microscopic level).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:434:y:2015:i:c:p:201-210
    DOI: 10.1016/j.physa.2015.03.021
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    References listed on IDEAS

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    1. 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.
    2. Geoffrey B. West & James H. Brown & Brian J. Enquist, 2001. "A general model for ontogenetic growth," Nature, Nature, vol. 413(6856), pages 628-631, October.
    3. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
    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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    Cited by:

    1. Ribeiro, Fabiano L. & Li, Yunfei & Born, Stefan & Rybski, Diego, 2024. "Analytical solution for the long- and short-range every-pair-interactions system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Netto, Vinicius M. & Brigatti, Edgardo & Meirelles, João & Ribeiro, Fabiano L. & Pace, Bruno & Cacholas, Caio & Sanches, Patricia Mara, 2018. "Cities, from information to interaction," SocArXiv jgz5d, Center for Open Science.
    3. Jiang, Wuhao & Wang, Kai & Lv, Yan & Guo, Jianfeng & Ni, Zhongjin & Ni, Yihua, 2020. "Time series based behavior pattern quantification analysis and prediction — A study on animal behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Netto, Vinicius M. & Meirelles, João Vitor & Ribeiro, Fabiano L., 2017. "Social Interaction and the City: The Effect of Space on the Reduction of Entropy," SocArXiv kdfkt, Center for Open Science.
    5. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    6. Vinicius M. Netto & Joao Meirelles & Fabiano L. Ribeiro, 2017. "Social Interaction and the City: The Effect of Space on the Reduction of Entropy," Complexity, Hindawi, vol. 2017, pages 1-16, August.

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