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Dynamics of a three species food chain model with Crowley–Martin type functional response

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  • Upadhyay, Ranjit Kumar
  • Naji, Raid Kamel

Abstract

In this paper, a three species food chain model, consisting of a hybrid type of prey-dependent and predator-dependent functional responses, is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence conditions are established. Bifurcation diagrams are obtained for biologically feasible parameters. The results show that the system exhibits rich complexity features such as stable, periodic and chaotic dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1337-1346
    DOI: 10.1016/j.chaos.2009.03.020
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Shivam, & Singh, Kuldeep & Kumar, Mukesh & Dubey, Ramu & Singh, Teekam, 2022. "Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    3. Nitu Kumari & Nishith Mohan, 2019. "Cross Diffusion Induced Turing Patterns in a Tritrophic Food Chain Model with Crowley-Martin Functional Response," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    4. Souna, Fethi & Lakmeche, Abdelkader & Djilali, Salih, 2020. "Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
    6. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    7. Drubi, Fátima & Ibáñez, Santiago & Pilarczyk, Paweł, 2021. "Nilpotent singularities and chaos: Tritrophic food chains," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Kumar, Vikas & Kumari, Nitu, 2021. "Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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