Cover
Vol. 16 No. Special Issue (2020)

Published: June 30, 2020

Pages: 99-104

Conference Article

Synchronization and tracking control of a novel 3 dimensional chaotic system

Basil H. Jasim 1 Mofeed Turky Rashid Khulood Moosa Omran
1Electrical Engineering Department, University of Basrah, Basrah, Iraq
History
  • Received: April 30, 2020
  • Available Online: June 30, 2020
DOI

https://doi.org/10.37917/ijeee.sceeer.3rd.14

Abstract

In this article, a novel three dimensional chaotic systems is presented. An extensive analysis including Lyapunov exponents, dissipation, symmetry, rest points with their properties is introduced. An adaptive tracking control system for the proposed chaos system has been designed. Also, synchronization system for two identical systems has been designed. The simulation results showed the effectiveness of the designed tracking and synchronization control systems.

Keywords

References

  1. Ahmad Azar, Sundarapandian Vaidyanathan, (2015), “Chaos Modeling and Control Systems Design”, 2015. DOI: 10.1007/978-3-319-13132-0.
  2. Saeed Khorashadizadeh, Mohammad-Hassan Majidi, “Chaos synchronization using the Fourier series expansion with application to secure communications”, AEU - International Journal of Electronics and Communications, Vol. 82, 2017.
  3. Ghaida Al-Suhail, Fadhil Tahir, Mariam Abd, Viet- Thanh Pham, Luigi Fortuna, “Modelling of Long-Wave Chaotic Radar System for Anti-Stealth Applications”, Jasim, Rashid & Omran Communications in Nonlinear Science and Numerical Simulation, Vol. 57, 2017.
  4. Amin Yousefpour, Hadi Jahanshahi, J.M. Munoz- Pacheco, Stelios Bekiros, Zhouchao Wei, (2019), “A fractional-order hyper-chaotic economic system with transient chaos”, Chaos Solitons & Fractals, Vol. 130, 2019. DOI: 10.1016/j.chaos.2019.109400.
  5. Philippe Faradja, Guoyuan Qi, “Analysis of multistability, hidden chaos and transient chaos in brushless DC motor”, Chaos Solitons & Fractals, 2020. DOI: 132. 10.1016/j.chaos.2020.109606.
  6. Miillin T, “Chaos in physical systems. In: Crilly AJ, Earnshow RA, Jones H, edi- tors”, Fractals and chaos. New York: Springer, 1991, pp. 237–245.
  7. Shinbrot T, Grebogi C, Wisdom J, Yorke JA. “Chaos in a double pendulum”, Am J Phys, Vol. 60, Issue 6, 1992.
  8. Zhu Q, Ishitobi M, “Experimental study of chaos in a driven triple pendulum”, J Sound Vib, Vol. 227, Issue 1, 1999.
  9. Hemati N, “Strange attractors in brushless DC motors”, IEEE Trans Circuits Syst, Vol. 41, Issue 1, 1994.
  10. Emad Mahmoud, Fatimah Abood, “A novel sort of adaptive complex synchronizations of two indistinguishable chaotic complex nonlinear models with uncertain parameters and its applications in secure communications”, Results in Physics, Vol. 7, 2017. DOI: 10.1016/j.rinp.2017.07.050.
  11. Amin Yousefpour, Hadi Jahanshahi, J.M. Munoz- Pacheco, Stelios Bekiros, Zhouchao Wei, “A fractional- order hyper-chaotic economic system with transient chaos. Chaos Solitons & Fractals, Vol. 130, 2019. DOI: 10.1016/j.chaos.2019.109400.
  12. Emad Mahmoud, “Dynamics and synchronization of new hyperchaotic complex Lorenz system”, Mathematical and Computer Modelling, Vol. 55, 2012. DOI: 10.1016/j.mcm.2011.11.053.
  13. Maitreyee Dutta, Krishna Binoy, Roy, “A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation”, Chaos Solitons & Fractals, Vol. 130, 2020. DOI: 109414. 10.1016/j.chaos.2019.109414.
  14. Mohammad Ababneh, “A new four-dimensional chaotic attractor”, Ain Shams Engineering Journal, Vol. 9, 2016. DOI: 10.1016/j.asej.2016.08.020.
  15. Sundarapandian Vaidyanathan, Aceng Sambas, Mustafa Mamat, W. S. Mada Sanjaya, “A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot”, Archives of Control Sciences, Vol. 27, 2017. DOI: 10.1515/acsc- 2017-0032.
  16. E.N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Phys., Vol. 20, pp 131-141, 1963.
  17. Mohammad Ababneh, “A new four-dimensional chaotic attractor. Ain Shams Engineering Journal, Vol. 9, 2017. DOI: 10.1016/j.asej.2016.08.020.
  18. Homayoon Arabyani, Hassan Saberi-Nik, “Synchronisation of the hyperchaotic complex Lorenz system in a finite time”, International Journal of Modelling, Identification and Control, Vol. 25, 2016. DOI: 138. 10.1504/IJMIC.2016.075273.
  19. L.M. Pecora, T.L. Carroll, “Synchronization in chaotic systems”, Phys. Rev. Lett., Vol. 64, pp 821-824, 1990.
  20. Mengjiao Wang, Xiaohan Liao, Yong Deng, Li Zhijun, Yongxin Su, Yicheng Zeng, “Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors”, Chaos, Solitons & Fractals, Vol. 130, 2020. DOI: 109406. 10.1016/j.chaos.2019.109406.
  21. Wolf A, Swift J, Swinney H, Vastano J., “Determing Lyapunov exponents from a time series”, Phys Lett B, Vol. 737, 1985.
  22. P. Frederickson, J.L. Kaplan, E.D. Yorke, J.A. Yorke, “The Liapunov dimension of strange attractors”, J. Differ. Equ., Vol. 44, pp. 185–207, 1983.