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Dynamical Study of Fractional Model of Allelopathic Stimulatory Phytoplankton Species

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Abstract

In this paper, we present a fractional model of interacting phytoplankton species in which one species produces chemical which is stimulatory in nature to the other species. We study existence, uniqueness, permanence, persistence and stability of the solution. We introduce a new method to prove permanence and persistence, which may be applicable to several ecological models of fractional order. At the end we propose a discritization method and perform some numerical simulations to validate our analytical findings.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi,  175001, Himachal Pradesh, India

    Syed Abbas & Lakshman Mahto

  2. Dipartimento di Matematica, Universita di Bologna, Pizza di Porta S. Donato, 5, 40126,  Bologna, Italy

    Angelo Favini

  3. Laboratory of Applied Mathematics, Mohamed Khider University, PO Box 145, 07000,  Biskra, Algeria

    Mokhtar Hafayed

Authors
  1. Syed Abbas
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  2. Lakshman Mahto
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  3. Angelo Favini
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  4. Mokhtar Hafayed
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Correspondence to Syed Abbas.

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Abbas, S., Mahto, L., Favini, A. et al. Dynamical Study of Fractional Model of Allelopathic Stimulatory Phytoplankton Species. Differ Equ Dyn Syst 24, 267–280 (2016). https://doi.org/10.1007/s12591-014-0219-5

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  • DOI: https://doi.org/10.1007/s12591-014-0219-5

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