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Chaos in a three-cell population cancer model with variable-order fractional derivative with power, exponential and Mittag-Leffler memories

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  • Kachia, Krunal
  • Solís-Pérez, J.E.
  • Gómez-Aguilar, J.F.

Abstract

In this work, a three-dimensional cancer model which includes the interactions between tumor cells, healthy tissue cells, and activated immune system cells was considered via Liouville–Caputo, Caputo–Fabrizio, Atangana–Baleanu, and fractional conformable derivative. We show a numerical method based on two-step Lagrange polynomial interpolation to achieve numerical approximations to these derivatives. Besides, also we analyze the dynamics observed via sensitivity to initial conditions, Lyapunov exponent estimation, square sum error, and phase-space diagrams. Novel attractors were obtained and all of them depicted novel chaotic behaviors by choosing a fractional variable-order.

Suggested Citation

  • Kachia, Krunal & Solís-Pérez, J.E. & Gómez-Aguilar, J.F., 2020. "Chaos in a three-cell population cancer model with variable-order fractional derivative with power, exponential and Mittag-Leffler memories," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305737
    DOI: 10.1016/j.chaos.2020.110177
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    References listed on IDEAS

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    1. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    2. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Shaobo He & Santo Banerjee & Bo Yan, 2018. "Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System," Complexity, Hindawi, vol. 2018, pages 1-15, August.
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    Cited by:

    1. Yi Wang & Zhaoyan Wu, 2021. "Cluster Synchronization in Variable-Order Fractional Community Network via Intermittent Control," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    2. Li, Ruihong & Li, Xingxin & Gan, Qintao & Wu, Huaiqin & Cao, Jinde, 2023. "Finite time event-triggered consensus of variable-order fractional multi-agent systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Cai, Wei & Wang, Zhouquan & Wang, Fajie, 2024. "Temperature and strain-rate dependent fractional constitutive model for glassy polymers," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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