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Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model

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  • Gómez-Aguilar, J.F.

Abstract

In this paper, we obtain novel chaotic behaviors using differential and integral operators with power-law, exponential-decay and Mittag-Leffler law for the Shinriki’s oscillator model. We studied the uniqueness and existence of the solutions employing the fixed point postulate. Also, we consider fractal–fractional operators to capture self-similarities for this chaotic attractor. These novel operators predict chaotic behaviors involving the fractal derivative in convolution with power-law, exponential decay law and the Mittag-Leffler function. The generalized model with power-law and Mittag-Leffler kernel was solved numerically via the Adams–Bashforth–Moulton and Adams–Moulton scheme, respectively. For another cases, the numerical schemes are based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. Numerical simulations for the symmetric and asymmetric cases are obtained to show the applicability and computational efficiency of these methods.

Suggested Citation

  • Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    • Handle: RePEc:eee:phsmap:v:539:y:2020:i:c:s0378437119316541
    DOI: 10.1016/j.physa.2019.122918
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    References listed on IDEAS

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    1. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
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    4. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    5. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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    Cited by:

    1. Ramadoss, Janarthanan & Kengne, Jacques & Kengnou Telem, Adélaïde Nicole & Rajagopal, Karthikeyan, 2022. "Broken symmetry and dynamics of a memristive diodes bridge-based Shinriki oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    2. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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