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Effects of a Fluctuating Carrying Capacity on the Generalized Malthus‐Verhulst Model

Author

Listed:
  • Héctor Calisto
  • Kristopher J. Chandía
  • Mauro Bologna

Abstract

We consider a generalized Malthus‐Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity.

Suggested Citation

  • Héctor Calisto & Kristopher J. Chandía & Mauro Bologna, 2014. "Effects of a Fluctuating Carrying Capacity on the Generalized Malthus‐Verhulst Model," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:597012
    DOI: 10.1155/2014/597012
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    References listed on IDEAS

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    1. A. Dubkov & B. Spagnolo, 2008. "Verhulst model with Lévy white noise excitation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 361-367, October.
    2. Shapiro, V.E. & Loginov, V.M., 1978. "“Formulae of differentiation” and their use for solving stochastic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 563-574.
    3. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    4. M. Bologna & H. Calisto, 2011. "Effects on generalized growth models driven by a non-Poissonian dichotomic noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 83(3), pages 409-414, October.
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