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Chaos in a three-species food chain model with a Beddington–DeAngelis functional response

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  • Zhao, Min
  • Lv, Songjuan

Abstract

This paper investigates a three-species food chain model with a Beddington–DeAngelis functional response, both analytically and through numerical simulations. First the equilibrium states of the system are identified and their stability analyzed analytically. The results of simulations demonstrate chaotic long-term behavior over a broad range of parameters. The existence of a strange attractor and computation of the largest Lyapunov exponent also demonstrate the presence of chaotic dynamics in the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2305-2316
    DOI: 10.1016/j.chaos.2007.10.025
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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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    7. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaos in a new system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1203-1212.
    8. Hui, Jing & Chen, Lansun, 2006. "Dynamic complexities in a periodically pulsed ratio-dependent predator–prey ecosystem modeled on a chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 407-416.
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    10. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 474-482.
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    Cited by:

    1. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar, 2014. "Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 50-63.
    2. Zhou, Hao & Tang, Sanyi, 2022. "Bifurcation dynamics on the sliding vector field of a Filippov ecological system," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    3. 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).
    4. Zhang, Limin & Zhao, Min, 2009. "Dynamic complexities in a hyperparasitic system with prolonged diapause for host," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1136-1142.
    5. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    6. Ali, Emad & Asif, Mohammed & Ajbar, AbdelHamid, 2013. "Study of chaotic behavior in predator–prey interactions in a chemostat," Ecological Modelling, Elsevier, vol. 259(C), pages 10-15.
    7. 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.
    8. Yujing Yang & Wenzhe Tang, 2018. "Research on a 3D Predator-Prey Evolutionary System in Real Estate Market," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    9. Xue, Lin, 2012. "Pattern formation in a predator–prey model with spatial effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5987-5996.
    10. 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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