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The chaos and optimal control of cancer model with complete unknown parameters

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  • El-Gohary, Awad
  • Alwasel, I.A.

Abstract

In this paper, we study the chaos and optimal control of cancer model with completely unknown parameters. The stability analysis of the biologically feasible steady-states of this model will be discussed. It is proved that the system appears to exhibit periodic and quasi-periodic limit cycles and chaotic attractors for some ranges of the system parameters. The necessary optimal controllers input for the asymptotic stability of some positive equilibrium states are derived. Numerical analysis and extensive numerical examples of the uncontrolled and controlled systems were carried out for various parameters values and different initial densities.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2865-2874
    DOI: 10.1016/j.chaos.2009.04.028
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    References listed on IDEAS

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    1. 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.
    2. Menchón, S.A. & Ramos, R.A. & Condat, C.A., 2007. "Modeling subspecies and the tumor-immune system interaction: Steps toward understanding therapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 713-719.
    3. El-Gohary, Awad, 2008. "Chaos and optimal control of cancer self-remission and tumor system steady states," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1305-1316.
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    Cited by:

    1. Mohammad Shahzad, 2016. "Chaos Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra," Mathematics, MDPI, vol. 4(2), pages 1-11, May.
    2. Mohammadi, Shaban & Hejazi, S. Reza, 2023. "Using particle swarm optimization and genetic algorithms for optimal control of non-linear fractional-order chaotic system of cancer cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 538-560.
    3. Das, Parthasakha & Das, Samhita & Upadhyay, Ranjit Kumar & Das, Pritha, 2020. "Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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