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Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

Author

Listed:
  • Luis M. Abia

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Óscar Angulo

    (Departamento de Matemática Aplicada, ETS de Ingenieros de Telecomunicación, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Juan Carlos López-Marcos

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Miguel Ángel López-Marcos

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

Abstract

The dynamics of a specific consumer-resource model for Daphnia magna is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.

Suggested Citation

  • Luis M. Abia & Óscar Angulo & Juan Carlos López-Marcos & Miguel Ángel López-Marcos, 2021. "Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2746-:d:667734
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    Cited by:

    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.

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