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Dynamics of a three-species food chain model with adaptive traits

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  • Sun, Chengjun
  • Loreau, Michel

Abstract

A three-species food chain model is proposed with dynamically variable adaptive traits in the intermediate consumer. We prove that its solutions are non-negative and bounded, and we analyze the existence and stability of its equilibria. By applying Li and Muldowney’s [Li MY, Muldowney J. On Bendixson’s criterion. J Differ Equ 1993;106:27–39] high-dimensional Bendixson criterion, we show that the positive equilibrium is globally stable under specific conditions. We support our analytical findings with numerical simulations.

Suggested Citation

  • Sun, Chengjun & Loreau, Michel, 2009. "Dynamics of a three-species food chain model with adaptive traits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2812-2819.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2812-2819
    DOI: 10.1016/j.chaos.2008.10.015
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
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    4. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    5. Sun, Chengjun & Han, Maoan & Lin, Yiping & Chen, Yuanyuan, 2007. "Global qualitative analysis for a predator–prey system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1582-1596.
    6. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
    7. Gomes, A.A. & Manica, E. & Varriale, M.C., 2008. "Applications of chaos control techniques to a three-species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 1097-1107.
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