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A chaos control strategy for the fractional 3D Lotka–Volterra like attractor

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  • Naik, Manisha Krishna
  • Baishya, Chandrali
  • Veeresha, P.

Abstract

In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established.

Suggested Citation

  • Naik, Manisha Krishna & Baishya, Chandrali & Veeresha, P., 2023. "A chaos control strategy for the fractional 3D Lotka–Volterra like attractor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 1-22.
    • Handle: RePEc:eee:matcom:v:211:y:2023:i:c:p:1-22
    DOI: 10.1016/j.matcom.2023.04.001
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    References listed on IDEAS

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    1. Yong Xu & Hua Wang, 2013. "Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
    2. Wang, Junwei & Xiong, Xiaohua & Zhang, Yanbin, 2006. "Extending synchronization scheme to chaotic fractional-order Chen systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 279-285.
    3. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    4. Zhen Wang, 2013. "Synchronization of an Uncertain Fractional-Order Chaotic System via Backstepping Sliding Mode Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-6, June.
    5. Karthikeyan Rajagopal & Anitha Karthikeyan & Prakash Duraisamy, 2017. "Hyperchaotic Chameleon: Fractional Order FPGA Implementation," Complexity, Hindawi, vol. 2017, pages 1-16, May.
    6. Mamadou Diouf & Ndolane Sene, 2020. "Analysis of the Financial Chaotic Model with the Fractional Derivative Operator," Complexity, Hindawi, vol. 2020, pages 1-14, June.
    7. Dadras, Sara & Momeni, Hamid Reza, 2010. "Control of a fractional-order economical system via sliding mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2434-2442.
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    Cited by:

    1. Zhi Liu & Rongwei Guo, 2023. "Stabilization of the GLV System with Asymptotically Unbounded External Disturbances," Mathematics, MDPI, vol. 11(21), pages 1-12, October.
    2. Maciej Leszczynski & Przemyslaw Perlikowski & Piotr Brzeski, 2024. "A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method," Mathematics, MDPI, vol. 12(7), pages 1-19, March.

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