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Modelling discrete time fractional Rucklidge system with complex state variables and its synchronization

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  • Vignesh, D.
  • He, Shaobo
  • Banerjee, Santo

Abstract

This article proposes a discrete time fractional order three dimensional Rucklidge system with complex state variables. The dynamical nature and chaotic behavior exhibited by the Rucklidge system with real state variables and higher dimensional system derived from complex state variables are compared. The stability of the proposed system is analyzed at their equilibrium states by obtaining eigenvalues numerically. Chaotic dynamics exhibited by the system with real and complex variables are investigated employing different methods like bifurcation analysis and maximum Lyapunov exponents via the Jacobian matrix method. Nonlinear controllers are introduced for chaos synchronization of the subsystems of the proposed discrete time Rucklidge system with fractional order. The article further discusses the coexisting behavior of the attractors for the Rucklidge system of real state variables with coexisting bifurcation diagrams. The impact of the parameters on the system dynamics is demonstrated with a sequence of bifurcation diagrams for the simultaneous variation of two parameters.

Suggested Citation

  • Vignesh, D. & He, Shaobo & Banerjee, Santo, 2023. "Modelling discrete time fractional Rucklidge system with complex state variables and its synchronization," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    • Handle: RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002801
    DOI: 10.1016/j.amc.2023.128111
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    References listed on IDEAS

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    1. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    3. Chao Luo & Xingyuan Wang, 2013. "Chaos Generated From The Fractional-Order Complex Chen System And Its Application To Digital Secure Communication," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-23.
    4. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Cuimei Jiang & Shutang Liu & Chao Luo, 2014. "A New Fractional-Order Chaotic Complex System and Its Antisynchronization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, October.
    6. Ran, Jie & Li, Yu-Qin & Xiong, Yi-Bin, 2022. "On the dynamics of fractional q-deformation chaotic map," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    7. Wang, Xia, 2009. "Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2208-2217.
    8. Cánovas, Jose S. & Rezgui, Houssem Eddine, 2023. "Revisiting the dynamic of q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
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