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On the dynamical behavior of three species food web model

Author

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  • Naji, R.K.
  • Balasim, A.T.

Abstract

In this paper, a mathematical model consisting of two preys one predator with Beddington–DeAngelis functional response is proposed and analyzed. The local stability analysis of the system is carried out. The necessary and sufficient conditions for the persistence of three species food web model are obtained. For the biologically reasonable range of parameter values, the global dynamics of the system has been investigated numerically. Number of bifurcation diagrams has been obtained; Lyapunov exponents have been computed for different attractor sets. It is observed that the model has different types of attractors including chaos.

Suggested Citation

  • Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1636-1648
    DOI: 10.1016/j.chaos.2006.04.064
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    Citations

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    Cited by:

    1. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Ivanov, Tihomir & Dimitrova, Neli, 2017. "A predator–prey model with generic birth and death rates for the predator and Beddington–DeAngelis functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 111-123.
    3. Cai, Liming & Li, Xuezhi & Yu, Jingyuan & Zhu, Guangtian, 2009. "Dynamics of a nonautonomous predator–prey dispersion–delay system with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2064-2075.
    4. Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    5. Gupta, R.P. & Yadav, Dinesh K., 2023. "Nonlinear dynamics of a stage-structured interacting population model with honest signals and cues," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Upadhyay, Ranjit Kumar & Naji, Raid Kamel, 2009. "Dynamics of a three species food chain model with Crowley–Martin type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1337-1346.
    7. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.
    9. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.

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