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Dynamical analysis and chaos control of the fractional chaotic ecological model

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  • Mahmoud, Emad E.
  • Trikha, Pushali
  • Jahanzaib, Lone Seth
  • Almaghrabi, Omar A.

Abstract

In this paper the fractional version of the proposed integer order chaotic ecological system is studied. Here chaos has been observed in the competitive ecological model due to linear and nonlinear interactions among various species considering shortage of food resources. The system being important constituent of the food supply chain is analyzed using tools of dynamics viz. Lyapunov dynamics, bifurcation diagrams, existence and uniqueness of solution, the fixed point analysis and effect of fractional order on the dynamics of the system. In the presence of uncertainties and disturbances the chaos in the F.O. ecological model is controlled using adaptive SMC theory about its two fixed points. Numerical illustrations have been provided using MATLAB.

Suggested Citation

  • Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307438
    DOI: 10.1016/j.chaos.2020.110348
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    References listed on IDEAS

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    1. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Bo Li & Xiaobing Zhou & Yun Wang, 2019. "Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems," Complexity, Hindawi, vol. 2019, pages 1-9, November.
    4. Pushali Trikha & Lone Seth Jahanzaib, 2020. "Dynamical Analysis of a Novel 4-D Hyper-Chaotic System With One Non-Hyperbolic Equilibrium Point and Application in Secure Communication," International Journal of System Dynamics Applications (IJSDA), IGI Global, vol. 9(4), pages 74-99, October.
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    Cited by:

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    2. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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