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Chaos and adaptive control in two prey, one predator system with nonlinear feedback

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  • El-Gohary, Awad
  • Al-Ruzaiza, A.S.

Abstract

We show that the continuous time three species prey–predator populations can be asymptotically stabilized using a nonlinear feedback control inputs. The necessary feedback control law for asymptotic stability of this system is obtained. The system appears to exhibit a chaotic behavior for a range of parametric values. The range of the system parameters for which the subsystems converge to limit cycles is determined. The results of some other models in the literature can be obtained as special cases of the present model. Numerical examples and analysis of the results are presented.

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  • El-Gohary, Awad & Al-Ruzaiza, A.S., 2007. "Chaos and adaptive control in two prey, one predator system with nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 443-453.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:443-453
    DOI: 10.1016/j.chaos.2006.03.101
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    References listed on IDEAS

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    1. Lipowski, Adam & Lipowska, Dorota, 2000. "Nonequilibrium phase transition in a lattice prey–predator system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 456-464.
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    Cited by:

    1. El-Gohary, Awad, 2009. "Chaos and optimal control of equilibrium states of tumor system with drug," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 425-435.
    2. Ma, Zhan-Ping & Yue, Jia-Long, 2023. "Cross diffusion induced spatially inhomogeneous Hopf bifurcation for a three species Lotka–Volterra food web model with cycle," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Uğur Erkin Kocamaz & Alper Göksu & Harun Taşkın & Yılmaz Uyaroğlu, 2021. "Control of chaotic two-predator one-prey model with single state control signals," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1563-1572, August.
    4. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
    5. El-Gohary, Awad & Alwasel, I.A., 2009. "The chaos and optimal control of cancer model with complete unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2865-2874.

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