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Caputo fractional standard map: Scaling invariance analyses

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  • Borin, Daniel

Abstract

In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order 1<α<2 considered on a cylinder. We consider relatively large values of the nonlinearity parameter K for which the map is chaotic. The survival probability has a short plateau followed by an exponential decay and is scaling invariant for all considered values of α and K.

Suggested Citation

  • Borin, Daniel, 2024. "Caputo fractional standard map: Scaling invariance analyses," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001486
    DOI: 10.1016/j.chaos.2024.114597
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    1. Ze-Yu Liu & Tiecheng Xia & Yi-Ping Wang, 2021. "Fractional Quantum Logistic Map And Its Application In Image Encryption Technology," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-16, November.
    2. Laskin, Nick, 2017. "Time fractional quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 16-28.
    3. Méndez-Bermúdez, J.A. & Peralta-Martinez, Kevin & Sigarreta, José M. & Leonel, Edson D., 2023. "Leaking from the phase space of the Riemann–Liouville fractional standard map," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Meng-Hui Wang & Her-Terng Yau, 2014. "New Power Quality Analysis Method Based on Chaos Synchronization and Extension Neural Network," Energies, MDPI, vol. 7(10), pages 1-18, October.
    5. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    6. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    7. Borin, Daniel & Livorati, André Luís Prando & Leonel, Edson Denis, 2023. "An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    9. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    10. Lim, S.C., 2006. "Fractional derivative quantum fields at positive temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 269-281.
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