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Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel

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  • Owolabi, Kolade M.
  • Gómez-Aguilar, J.F.
  • Karaagac, Berat

Abstract

In this paper, a range of chaotic systems with some interesting behaviors such as multi-scroll attractors, self-excited and hidden attractors, period-doubling to chaos, periodic and chaotic bursting oscillations, and different multiple coexisting attractors have been considered and modelled with the new Atangana–Baleanu fractional derivative operator in time. Existence and uniqueness of general system as well as local stability analysis are examined. In the simulation framework, a range of chaotic patterns examined through time series were obtained for different instances of fractional orders. Comparison between the integer (with p=1) and noninteger (0 < p < 1) order results are given.

Suggested Citation

  • Owolabi, Kolade M. & Gómez-Aguilar, J.F. & Karaagac, Berat, 2019. "Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 54-63.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:54-63
    DOI: 10.1016/j.chaos.2019.05.019
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
    2. Cao, Yang & Samidurai, R. & Sriraman, R., 2019. "Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 57-77.
    3. Cao, Yang, 2019. "Bifurcations in an Internet congestion control system with distributed delay," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 54-63.
    4. Owolabi, Kolade M. & Gómez-Aguilar, J.F., 2018. "Numerical simulations of multilingual competition dynamics with nonlocal derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 175-182.
    5. Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    6. Owolabi, Kolade M., 2018. "Analysis and numerical simulation of multicomponent system with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 127-134.
    7. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
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