Author:
Tagne Samuel,Bodo Bertrand,Eyebe Guy François V. Ayissi,Fouda Jean Sire A. Eyebe
Abstract
AbstractThe paper studies a 3D Chaotic Jerk oscillator with fractional derivatives. An approach is proposed to implement it on a PIC16F877A microcontroller in order to reduce the requirements for multiple analogue electronic components such as resistors, capacitors, coils, multipliers, operational amplifiers, which are very bulky and consume a lot of power. The behaviours of the underlying system are analysed analytically, numerically and experimentally. It comes from this analysis that the fractional model exhibits chaotic dynamics when for parameters for which the equivalent integer derivative system exhibits limit-cycles. The synchronization under two closed initial conditions is also studied, highlighting one of the most common applications of the chaos concept.
Publisher
Springer Science and Business Media LLC
Reference60 articles.
1. José Francisco, G.-A., Juan, R.-G., Manuel, G.-C., José Roberto, R.-H. Fractional RC and LC electrical circuits. Ingenierí a Investigació n y Tecnologí a. 15(2), 311–319. https://doi.org/10.1016/S1405-7743(14)72219-X. (2014) (ISSN 1405-7743).
2. Riewe, F. Mechanics with fractional derivatives. Phys. Rev. E. 55, 3581–3592. https://doi.org/10.1103/PhysRevE.55.3581 (1997).
3. Hammad, M. M., Yaqut, A. S. H., Abdel-Khalek, M. A. & Doma, S. B. Analytical study of conformable fractional Bohr Hamiltonian with Kratzer potential. Nucl. Phys. A. 1015, 122307. https://doi.org/10.1016/j.nuclphysa.2021.122307 (2021) (ISSN 0375-9474).
4. J. (Eds.) Kumar, S. Fractional Calculus in Medical and Health Science, 1st ed. https://doi.org/10.1201/9780429340567 (CRC Press, 2020).
5. Chu, Y.-M., Hadi, S.-B., Oumate, J., Abba, A., Solis-Pé rez, J. E., Bekiros, S., Gomez-Aguilar, J. F., Yousefpour, A. The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization. Chaos Solut. Fractals (2020).
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献